Maths-
General
Easy

Question

Dimensions of the cuboid are in the ratio of 5 : 4: 2 and the whole surface area is 684 cm2, find the volume of the cuboid?

  1. 1080
  2. 2020
  3. 1000
  4. 1560

Hint:

Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
Volume of a cuboid = l × b × h    [cubic units]
Where,
l = length
b = breadth
h = height

The correct answer is: 1080


    We are given that

    Length, breadth and height of a cuboid are in the ratio 5:4:2 and the total surface area is 684 cm2,

    Let, the dimension of cuboid are

    l = 5x,

    b = 4x

    and h = 2x

    Now,

    Surface area of cuboid = 2((5x cross times4x) + (4xcross times2x) + (2xcross times5x))

    = 2((20x2)+(8x2)+(10x2))

    = 2(38 x2)

    = 76x2

    Surface area of cuboid = 684

    76x= 684

    x= 9

    Now,

    x = 3

    Dimensions of cuboid are,

    l = 5x = 5cross times3 =15cm,

    b = 4x = 4cross times3 = 12cm

    h = 2x = 2cross times3 = 6cm

    Volume of cuboid = l cross timescross times h

    = 15 cross times 12 cross times 6

    = 1080 cm3

    Hence, the volume of cuboid is 1080 cm3 is the answer.

    Therefore , the correct option is a)1080

    Related Questions to study

    General
    Maths-

    Radius and slant height of a cone are 20 cm and 29 cm respectively. Find its volume

    Hint:- Volume of a cone = (1/3)πr2h
    By applying Pythagoras theorem  on the cone, we can find the relation between volume and slant height of the cone.
    We know, h2 + r2 = L2
    h equals square root of open parentheses L squared minus r squared close parentheses end root
    where,
    • h is the height of the cone,
    • r is the radius of the base, and,
    • L is the slant height of the cone.
    The volume of the cone in terms of slant height can be given as
    V equals left parenthesis 1 divided by 3 right parenthesis pi r squared h equals left parenthesis 1 divided by 3 right parenthesis pi r squared square root of blank end root open parentheses L squared minus r squared close parentheses
    Solution:- We have given that
    Radius, r = 20 cm
    Slant height , L = 29 cm
    Therefore, volume of cone = left parenthesis 1 divided by 3 with _ below right parenthesis m r squared square root of blank end root open parentheses L squared minus r squared close parentheses
    = (1/3)(3.14)(20 x 20) left parenthesis 1 divided by 3 with _ below right parenthesis straight capital pi r squared square root of blank end root open parentheses L squared minus r squared close parentheses
    = (1/3)(3.14)(400) √(841 - 400)
    = (1/3)(1256) √(441)
    = (1/3)(1256)(21)
    = 1256 x 7
    = 8792 cm3
    Therefore, the volume of given cone is 8792 cm3
    Therefore option c) 8792 cm3 is correct.

    Radius and slant height of a cone are 20 cm and 29 cm respectively. Find its volume

    Maths-General
    Hint:- Volume of a cone = (1/3)πr2h
    By applying Pythagoras theorem  on the cone, we can find the relation between volume and slant height of the cone.
    We know, h2 + r2 = L2
    h equals square root of open parentheses L squared minus r squared close parentheses end root
    where,
    • h is the height of the cone,
    • r is the radius of the base, and,
    • L is the slant height of the cone.
    The volume of the cone in terms of slant height can be given as
    V equals left parenthesis 1 divided by 3 right parenthesis pi r squared h equals left parenthesis 1 divided by 3 right parenthesis pi r squared square root of blank end root open parentheses L squared minus r squared close parentheses
    Solution:- We have given that
    Radius, r = 20 cm
    Slant height , L = 29 cm
    Therefore, volume of cone = left parenthesis 1 divided by 3 with _ below right parenthesis m r squared square root of blank end root open parentheses L squared minus r squared close parentheses
    = (1/3)(3.14)(20 x 20) left parenthesis 1 divided by 3 with _ below right parenthesis straight capital pi r squared square root of blank end root open parentheses L squared minus r squared close parentheses
    = (1/3)(3.14)(400) √(841 - 400)
    = (1/3)(1256) √(441)
    = (1/3)(1256)(21)
    = 1256 x 7
    = 8792 cm3
    Therefore, the volume of given cone is 8792 cm3
    Therefore option c) 8792 cm3 is correct.
    General
    Maths-

    The area of a base of a cuboid is 48 cm2 and its height and length of the diagonal are 3 cm and 13 cm respectively. Calculate the length and width of the box?

    Let a be the length and b be the width and c be height of rectangular solid whose area of the base will be (ab) m2 and

    length of diagonal = square root of a squared plus b squared plus c squared end root

    So accordingly

    (a)(b)=48 ……………..(1) and

    square root of a squared plus b squared plus c squared end root equals 13. text  or.  end text a squared plus b squared plus c squared equals 169

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a squared plus b squared equals 169 minus c squared end cell row cell a squared plus b squared equals 169 minus 9 end cell end table

    a2+b2=160-------------(2).

    Now using formula. (a + b)= a2+b2+2.ab

    (a + b)= 160 + 2 × 48

    (a + b)= 160 + 96 = 256

    Taking square root of both sides

    or. a + b = 16……………(3)

    and. (a - b)= a+ b- 2.ab

    ( a- b)= 160 – 96 = 64

    Taking square root of both sides

    or. a - b = 8…………………(4). ,

    By adding eqn. (3) and (4) we get,

    2a = 24.

    a = 24/2 = 12 m.

    Putting a = 12 in eqn. (3)

    12 + b = 16

    b = 16 – 12

    b = 4 m.

    Thus , length =12 m , width = 4 m.

    Therefore, the correct option is c)12cm , 4cm.

    The area of a base of a cuboid is 48 cm2 and its height and length of the diagonal are 3 cm and 13 cm respectively. Calculate the length and width of the box?

    Maths-General
    Let a be the length and b be the width and c be height of rectangular solid whose area of the base will be (ab) m2 and

    length of diagonal = square root of a squared plus b squared plus c squared end root

    So accordingly

    (a)(b)=48 ……………..(1) and

    square root of a squared plus b squared plus c squared end root equals 13. text  or.  end text a squared plus b squared plus c squared equals 169

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a squared plus b squared equals 169 minus c squared end cell row cell a squared plus b squared equals 169 minus 9 end cell end table

    a2+b2=160-------------(2).

    Now using formula. (a + b)= a2+b2+2.ab

    (a + b)= 160 + 2 × 48

    (a + b)= 160 + 96 = 256

    Taking square root of both sides

    or. a + b = 16……………(3)

    and. (a - b)= a+ b- 2.ab

    ( a- b)= 160 – 96 = 64

    Taking square root of both sides

    or. a - b = 8…………………(4). ,

    By adding eqn. (3) and (4) we get,

    2a = 24.

    a = 24/2 = 12 m.

    Putting a = 12 in eqn. (3)

    12 + b = 16

    b = 16 – 12

    b = 4 m.

    Thus , length =12 m , width = 4 m.

    Therefore, the correct option is c)12cm , 4cm.

    General
    Maths-

    Internal length, height, and breadth of an open box are 95 cm, 82 cm, and 75 cm. Thickness of wood is given to be 2.5 cm, calculate the cost of painting outside the box as Rs 1 per dm2

    We have given the Internal dimensions of the box
    length = 95 cm,
    breadth = 75 cm
    height = 82 cm
    Outer dimensions of the box are
    length = 95 + 2 cross times 2.5 = 100 cm,
    breadth = 75 + 2 cross times 2.5 = 80 cm
    height = 82 + 2.5 = 84.5 --as the box is open we will add only 2.5
    Surface area of the box = 2(lb+ bh +lh)

    = 2((95)(75)+(75)(82)+(95)(82))

    = 2(8000+6760+8450)=

    = 46420 cm2
    Surface area of the open box = Total area  - area of open side

    = 46420 – (95)(75)

    = 46420-8000

    = 38420 cm2

    = 384.2 dm2

    Cost of painting = Rs. 384.20
    Therefore option d) 384.20 is correct.

    Internal length, height, and breadth of an open box are 95 cm, 82 cm, and 75 cm. Thickness of wood is given to be 2.5 cm, calculate the cost of painting outside the box as Rs 1 per dm2

    Maths-General
    We have given the Internal dimensions of the box
    length = 95 cm,
    breadth = 75 cm
    height = 82 cm
    Outer dimensions of the box are
    length = 95 + 2 cross times 2.5 = 100 cm,
    breadth = 75 + 2 cross times 2.5 = 80 cm
    height = 82 + 2.5 = 84.5 --as the box is open we will add only 2.5
    Surface area of the box = 2(lb+ bh +lh)

    = 2((95)(75)+(75)(82)+(95)(82))

    = 2(8000+6760+8450)=

    = 46420 cm2
    Surface area of the open box = Total area  - area of open side

    = 46420 – (95)(75)

    = 46420-8000

    = 38420 cm2

    = 384.2 dm2

    Cost of painting = Rs. 384.20
    Therefore option d) 384.20 is correct.

    parallel
    General
    Maths-

    The total surface area of a cube is 846 cm2. Find the height, breadth, and length if the dimensions are in the ratio of 3:4:5

    We have given the surface area of cube = 846cm2
    And the ratio of height breadth and length is 3:4:5
    Let , height = 3x,
    Breadth =4x,
    Length = 5x
    Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
    2 left square bracket left parenthesis 5 x right parenthesis left parenthesis 4 x right parenthesis plus left parenthesis 4 x right parenthesis left parenthesis 3 x right parenthesis plus left parenthesis 5 x right parenthesis left parenthesis 3 x right parenthesis right square bracket equals 846

    2 open square brackets 20 x squared plus 12 x squared plus 15 x squared close square brackets equals 846
    2(47x2) = 846
    Divide both sides by 2,
    table attributes columnspacing 1em end attributes row cell 47 x squared equals 846 over 2 end cell row cell 47 x squared equals 423 end cell end table
    Divide both sides by 47,
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x squared equals 423 over 47 end cell row cell x squared equals 9 end cell end table
    Taking square root
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x equals square root of 9 end cell row cell x equals 3 end cell end table
    The dimensions of cuboid are,

    Height = 3x=3(3)= 9

    Breadth= 4x =4(3) =12

    Length = 5x = 5(3)= 15
    Therefore the option a)15cm , 12cm , 9cm is correct.

    The total surface area of a cube is 846 cm2. Find the height, breadth, and length if the dimensions are in the ratio of 3:4:5

    Maths-General
    We have given the surface area of cube = 846cm2
    And the ratio of height breadth and length is 3:4:5
    Let , height = 3x,
    Breadth =4x,
    Length = 5x
    Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
    2 left square bracket left parenthesis 5 x right parenthesis left parenthesis 4 x right parenthesis plus left parenthesis 4 x right parenthesis left parenthesis 3 x right parenthesis plus left parenthesis 5 x right parenthesis left parenthesis 3 x right parenthesis right square bracket equals 846

    2 open square brackets 20 x squared plus 12 x squared plus 15 x squared close square brackets equals 846
    2(47x2) = 846
    Divide both sides by 2,
    table attributes columnspacing 1em end attributes row cell 47 x squared equals 846 over 2 end cell row cell 47 x squared equals 423 end cell end table
    Divide both sides by 47,
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x squared equals 423 over 47 end cell row cell x squared equals 9 end cell end table
    Taking square root
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x equals square root of 9 end cell row cell x equals 3 end cell end table
    The dimensions of cuboid are,

    Height = 3x=3(3)= 9

    Breadth= 4x =4(3) =12

    Length = 5x = 5(3)= 15
    Therefore the option a)15cm , 12cm , 9cm is correct.

    General
    Maths-

    A cube of 11 cm edge is immersed completely in a rectangular vessel containing the liquid. If the dimensions of the base of the vessel are 12 cm and 15 cm, calculate the rise in the water level?

    • We know that,
    The dimensions of the base of the vessel are 15 cm × 12 cm
    l =15cm
    b = 12cm
    • Consider the rise in the water level = h cm
    • Volume of given cube = (11)3=1331
    • So the volume of cube = volume of the vessel
    • Substituting these values

    1331 = 15 × 12 × h

    • By further calculation

    h = 1331/ (15 × 12)

    • So we get

    h = 1331/ 180 = 7.39 cm

    • Therefore, the rise in the water level is 7.39 cm.
    • Therefore the correct option is b)7.39.

    A cube of 11 cm edge is immersed completely in a rectangular vessel containing the liquid. If the dimensions of the base of the vessel are 12 cm and 15 cm, calculate the rise in the water level?

    Maths-General
    • We know that,
    The dimensions of the base of the vessel are 15 cm × 12 cm
    l =15cm
    b = 12cm
    • Consider the rise in the water level = h cm
    • Volume of given cube = (11)3=1331
    • So the volume of cube = volume of the vessel
    • Substituting these values

    1331 = 15 × 12 × h

    • By further calculation

    h = 1331/ (15 × 12)

    • So we get

    h = 1331/ 180 = 7.39 cm

    • Therefore, the rise in the water level is 7.39 cm.
    • Therefore the correct option is b)7.39.
    General
    Maths-

    The circumference of the base of a 12 cm high wooden solid cone is 44 cm. Find the volume

    Hint:- Volume of a cone = (1 third)πr2h
    Circumference of base = 2πr
    Solution :- We have given the dimensions of a wooden solid cone
    Circumference = 44 m = 2πr
    44 = 2 (22 over 7) r
    r = (44 x 7) / 44
    r = 7
    Radius, r = 7 m
    Height, h = 12 m
    We have to find the volume of the given cone
    We know that
    Volume of a cup = (1/3)πr2h
    = (1 third)(3.14)(7 x 7)(12)
    = (1 third)(3.14) (49 x 12)
    = (1 third)(3.14)(588)
    = 1848 / 3
    = 616 cm3
    Therefore, the volume of wooden cone is 616 cm3
    Therefore correct option is a) 616 cm3.

    The circumference of the base of a 12 cm high wooden solid cone is 44 cm. Find the volume

    Maths-General
    Hint:- Volume of a cone = (1 third)πr2h
    Circumference of base = 2πr
    Solution :- We have given the dimensions of a wooden solid cone
    Circumference = 44 m = 2πr
    44 = 2 (22 over 7) r
    r = (44 x 7) / 44
    r = 7
    Radius, r = 7 m
    Height, h = 12 m
    We have to find the volume of the given cone
    We know that
    Volume of a cup = (1/3)πr2h
    = (1 third)(3.14)(7 x 7)(12)
    = (1 third)(3.14) (49 x 12)
    = (1 third)(3.14)(588)
    = 1848 / 3
    = 616 cm3
    Therefore, the volume of wooden cone is 616 cm3
    Therefore correct option is a) 616 cm3.
    parallel
    General
    Maths-

    Given length, breadth, and height of a cuboid are 15 cm, 37.5 cm, and 48 cm. Find the cube edge whose given volume is equal to the volume of this cuboid. Also, calculate the length of the diagonal to the nearest natural number.

    We are given the dimensions of the cuboid
    Length = l = 15cm
    Breadth = b =37.5cm
    Height = h = 48cm
    Volume of a cuboid = l × b × h =
    = 15 × 37.5 × 48
    = 27000 cm3
    As from the given condition ,
    Volume of cube = volume of cuboid
    a3 = 27000
    a = cube root of 27000
    a = 30
    Therefore the length of diagonal = left parenthesis square root of 3 right parenthesisa
    = left parenthesis square root of 3 right parenthesis 30
    = (1.734 )30
    = 51.9
    = 52
    Therefore, the correct answer is d) 30cm , 52cm

    Given length, breadth, and height of a cuboid are 15 cm, 37.5 cm, and 48 cm. Find the cube edge whose given volume is equal to the volume of this cuboid. Also, calculate the length of the diagonal to the nearest natural number.

    Maths-General
    We are given the dimensions of the cuboid
    Length = l = 15cm
    Breadth = b =37.5cm
    Height = h = 48cm
    Volume of a cuboid = l × b × h =
    = 15 × 37.5 × 48
    = 27000 cm3
    As from the given condition ,
    Volume of cube = volume of cuboid
    a3 = 27000
    a = cube root of 27000
    a = 30
    Therefore the length of diagonal = left parenthesis square root of 3 right parenthesisa
    = left parenthesis square root of 3 right parenthesis 30
    = (1.734 )30
    = 51.9
    = 52
    Therefore, the correct answer is d) 30cm , 52cm
    General
    Maths-

    Vtotal = Vcone 1+Vcone 2 Find the volume of the composite solid.
    Use 3.14 for pi.

    We have given the dimensions of a Cones in the given figure
    For Cone 1
    Radius, r = 6 cm
    Height, h = 7 cm
    For Cone 2
    Radius, R = 10 cm
    Height, H = 6 cm
    We have to find the volume of the given cone
    We know that
    Volume of a Cone 1 = (1 third)πr2h
    = (1 third)(3.14)(6 x 6)(7)
    = (1 third)(3.14) (36 x 7)
    = (1 third)(3.14)(252)
    = 791.28 / 3
    = 263.76 cm3
    Volume of a Cone 1 = (1 third)πR2H
    = (1 third)(3.14)(10 x 10)(6)
    = (1 third)(3.14) (100 x 6)
    = (1 third)(3.14)(600)
    = 1884 over 3
    = 628 cm3
    We know that Vtotal=Vcone 1+Vcone 2
    Vtotal = 263.76 + 628 = 891.76 cm3
    Therefore, the total volume of the composite solid is 891.76 cm3
    Therefore correct option is a)891.76 cm3 .

    Vtotal = Vcone 1+Vcone 2 Find the volume of the composite solid.
    Use 3.14 for pi.

    Maths-General
    We have given the dimensions of a Cones in the given figure
    For Cone 1
    Radius, r = 6 cm
    Height, h = 7 cm
    For Cone 2
    Radius, R = 10 cm
    Height, H = 6 cm
    We have to find the volume of the given cone
    We know that
    Volume of a Cone 1 = (1 third)πr2h
    = (1 third)(3.14)(6 x 6)(7)
    = (1 third)(3.14) (36 x 7)
    = (1 third)(3.14)(252)
    = 791.28 / 3
    = 263.76 cm3
    Volume of a Cone 1 = (1 third)πR2H
    = (1 third)(3.14)(10 x 10)(6)
    = (1 third)(3.14) (100 x 6)
    = (1 third)(3.14)(600)
    = 1884 over 3
    = 628 cm3
    We know that Vtotal=Vcone 1+Vcone 2
    Vtotal = 263.76 + 628 = 891.76 cm3
    Therefore, the total volume of the composite solid is 891.76 cm3
    Therefore correct option is a)891.76 cm3 .
    General
    Maths-

    Given edges of the cubes as 3 cm, 4 cm, and 5 cm respectively. Its now melted and made into one single cube. Calculate the edge of a new cube.

    Let the cubes be A, B and C and their sides are x, y and z respectively
    x= 3cm
    y=4cm
    z= 5cm
    And let the side if final cube is w
    We will first add the volumes of the three cubes A, B and C
    Vol(A) + Vol(B) + Vol(C) = x3 + y3 + z3
    = 33 + 43 + 53
    = 27 + 64 + 125
    = 216
    The sum of volumes of cubes A , B and C is equal to the resultant cube we obtain by melting these three,
    Volume of final cube =  Vol(A) + Vol(B) + Vol(C)
    (w)3 = 216
    We know that 216 is the cube of 6
    Therefore, w = 6
    Therefore, the correct option is b) 6 .

    Given edges of the cubes as 3 cm, 4 cm, and 5 cm respectively. Its now melted and made into one single cube. Calculate the edge of a new cube.

    Maths-General
    Let the cubes be A, B and C and their sides are x, y and z respectively
    x= 3cm
    y=4cm
    z= 5cm
    And let the side if final cube is w
    We will first add the volumes of the three cubes A, B and C
    Vol(A) + Vol(B) + Vol(C) = x3 + y3 + z3
    = 33 + 43 + 53
    = 27 + 64 + 125
    = 216
    The sum of volumes of cubes A , B and C is equal to the resultant cube we obtain by melting these three,
    Volume of final cube =  Vol(A) + Vol(B) + Vol(C)
    (w)3 = 216
    We know that 216 is the cube of 6
    Therefore, w = 6
    Therefore, the correct option is b) 6 .
    parallel
    General
    Maths-

    Mike has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Which is closest to the volume of Mike’s cup?

    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a large plastic cup of Mike in shape of cone
    Radius, r = 3 in
    Height, h = 7 in
    We have to find the volume of the given cone
    We know that
    Volume of a cup = (1 third)πr2h
    = (1 third)(3.14)(3 x 3)(7)
    = (1 third)(3.14) (9 x 7)
    = (1 third)(3.14)(63)
    = 197.82 over 3
    = 65.94 in3
    = 66 in3
    Therefore, the volume of Mike’s cup is 66 in3
    Therefore correct option is c) 66 in3.

    Mike has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Which is closest to the volume of Mike’s cup?

    Maths-General
    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a large plastic cup of Mike in shape of cone
    Radius, r = 3 in
    Height, h = 7 in
    We have to find the volume of the given cone
    We know that
    Volume of a cup = (1 third)πr2h
    = (1 third)(3.14)(3 x 3)(7)
    = (1 third)(3.14) (9 x 7)
    = (1 third)(3.14)(63)
    = 197.82 over 3
    = 65.94 in3
    = 66 in3
    Therefore, the volume of Mike’s cup is 66 in3
    Therefore correct option is c) 66 in3.
    General
    Maths-

    The dimensions of a cubical box are in the ratio of 5:4:3.and the length of the diagonal is 10√2. Calculate the total surface area?

    We have given that, dimensions of cubical box are in the ratio of 5:4:3.
    Let the dimensions of the box are

    Length = 5x

    Breadth= 4x

    Height = 3x
    We have given diagonal , therefore we can write,
    square root of open parentheses l squared plus b squared plus h squared close parentheses end root equals 10 square root of 2
    Lets put the assumed values of length , breadth and height in the above equation,
    square root of left parenthesis 5 x right parenthesis squared plus left parenthesis 4 x right parenthesis squared plus left parenthesis 3 x right parenthesis squared end root equals 10 square root of 2
    square root of 25 x squared plus 16 straight x squared plus 9 straight x squared end root equals 10 square root of 2
    square root of 50 x squared end root equals 10 square root of 2
    We can write as square root of 50 x squared end root text  as  end text 5 square root of 2 x,
    5 square root of 2 x equals 10 square root of 2
    Divide both sides of equation by 5 square root of 2
    x = 2
    Therefore, the dimensions of cuboid are,
    Length = 5x = 5(2)= 10

    Breadth= 4x = 4(2) =8

    Height = 3x=3(2)= 6

    • Putting the values in the formula of surface area

    Area = 2[(10)(8) + (8)(6) + (6)(10)]

    = 2[80 + 48 + 60]

    = 2(188)

    Area =376
    Therefore, the correct option is b)376.

    The dimensions of a cubical box are in the ratio of 5:4:3.and the length of the diagonal is 10√2. Calculate the total surface area?

    Maths-General
    We have given that, dimensions of cubical box are in the ratio of 5:4:3.
    Let the dimensions of the box are

    Length = 5x

    Breadth= 4x

    Height = 3x
    We have given diagonal , therefore we can write,
    square root of open parentheses l squared plus b squared plus h squared close parentheses end root equals 10 square root of 2
    Lets put the assumed values of length , breadth and height in the above equation,
    square root of left parenthesis 5 x right parenthesis squared plus left parenthesis 4 x right parenthesis squared plus left parenthesis 3 x right parenthesis squared end root equals 10 square root of 2
    square root of 25 x squared plus 16 straight x squared plus 9 straight x squared end root equals 10 square root of 2
    square root of 50 x squared end root equals 10 square root of 2
    We can write as square root of 50 x squared end root text  as  end text 5 square root of 2 x,
    5 square root of 2 x equals 10 square root of 2
    Divide both sides of equation by 5 square root of 2
    x = 2
    Therefore, the dimensions of cuboid are,
    Length = 5x = 5(2)= 10

    Breadth= 4x = 4(2) =8

    Height = 3x=3(2)= 6

    • Putting the values in the formula of surface area

    Area = 2[(10)(8) + (8)(6) + (6)(10)]

    = 2[80 + 48 + 60]

    = 2(188)

    Area =376
    Therefore, the correct option is b)376.

    General
    Maths-

    Calculate the amount of ice cream this cone can hold (just to the top of the cone). Round to the nearest hundredth.

    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a ice cream cone
    Diameter = 4.5 cm
    Radius , r = 4.5 over 2 = 2.25 cm
    Height , h = 11 cm
    We have to find the volume of the given cone
    We know that
    Volume of a cup = (1/3)πr2h
    = (1 third)(3.14)(2.25 x 2.25)(11)
    = (1 third)(3.14) (5.06 x 11)
    = (1 third)(3.14)(55.68)
    = 174.85 over 3
    = 58.29 cm3
    Therefore, the volume of ice cream cone is 58.29 cm3
    Therefore correct option is a)58.29 cm3.

    Calculate the amount of ice cream this cone can hold (just to the top of the cone). Round to the nearest hundredth.

    Maths-General
    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a ice cream cone
    Diameter = 4.5 cm
    Radius , r = 4.5 over 2 = 2.25 cm
    Height , h = 11 cm
    We have to find the volume of the given cone
    We know that
    Volume of a cup = (1/3)πr2h
    = (1 third)(3.14)(2.25 x 2.25)(11)
    = (1 third)(3.14) (5.06 x 11)
    = (1 third)(3.14)(55.68)
    = 174.85 over 3
    = 58.29 cm3
    Therefore, the volume of ice cream cone is 58.29 cm3
    Therefore correct option is a)58.29 cm3.
    parallel
    General
    Maths-

    Given dimensions of the room are 24 cm in breadth, 30 cm in height and 18 cm in length. Find the length of the longest pole that can be placed in the room

    We have given the dimensions of room
    Length l =18 cm
    Breadth b = 24cm
    Height h = 30cm
    To find the length of the longest pole that can be placed in the room
    We have formula = square root of open parentheses l squared plus b squared plus h squared close parentheses end root
    square root of 18 squared plus 24 squared plus 30 squared end root
    square root of 324 plus 576 plus 900 end root
    square root of 1800
    30 square root of 2
    = 42.426 cm

    Given dimensions of the room are 24 cm in breadth, 30 cm in height and 18 cm in length. Find the length of the longest pole that can be placed in the room

    Maths-General
    We have given the dimensions of room
    Length l =18 cm
    Breadth b = 24cm
    Height h = 30cm
    To find the length of the longest pole that can be placed in the room
    We have formula = square root of open parentheses l squared plus b squared plus h squared close parentheses end root
    square root of 18 squared plus 24 squared plus 30 squared end root
    square root of 324 plus 576 plus 900 end root
    square root of 1800
    30 square root of 2
    = 42.426 cm
    General
    Maths-

    Mr. Quintero has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Which is closest to the volume of Mr. Quintero's cup r = 3, h = 7

    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a large plastic cup of Mr. Quintero in shape of cone
    Radius, r = 3 in
    Height, h = 7 in
    We have to find the volume of the given cone
    We know that
    Volume of a cup = (1 third)πr2h
    = (1 third)(3.14)(3 x 3)(7)
    = (1 third)(3.14) (9 x 7)
    = (1 third)(3.14)(63)
    = 197.82 over 3
    = 65.94 in3
    = 66 in3
    Therefore, the volume of Mr. Quintero’s cup is 66 in3
    Therefore correct option is c) 66 in3.

    Mr. Quintero has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Which is closest to the volume of Mr. Quintero's cup r = 3, h = 7

    Maths-General
    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a large plastic cup of Mr. Quintero in shape of cone
    Radius, r = 3 in
    Height, h = 7 in
    We have to find the volume of the given cone
    We know that
    Volume of a cup = (1 third)πr2h
    = (1 third)(3.14)(3 x 3)(7)
    = (1 third)(3.14) (9 x 7)
    = (1 third)(3.14)(63)
    = 197.82 over 3
    = 65.94 in3
    = 66 in3
    Therefore, the volume of Mr. Quintero’s cup is 66 in3
    Therefore correct option is c) 66 in3.
    General
    Maths-

    Surface area of a cube is 443.76 cm2 . Find the volume of it?

    • We are given that 
    Surface area of a cube = 443.76 cm2
    • We have to find volume of the cube
    6a2 = 443.76
    • Divide both sides of equation by 6
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a squared equals fraction numerator 443.76 over denominator 6 end fraction end cell row cell a squared equals 73.96 end cell end table
    • Taking square root of both sides we get,
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a equals square root of 73.96 end root end cell row cell a equals 8.6 end cell end table
    • Therefore, the volume of the given cube is
    Volume = a3 = (8.6)3
    Volume = 636.056 cm3
    • The approximate of the volume is 6.4 from the given options,
    • Therefore the correct option is d) 6.4.

    Surface area of a cube is 443.76 cm2 . Find the volume of it?

    Maths-General
    • We are given that 
    Surface area of a cube = 443.76 cm2
    • We have to find volume of the cube
    6a2 = 443.76
    • Divide both sides of equation by 6
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a squared equals fraction numerator 443.76 over denominator 6 end fraction end cell row cell a squared equals 73.96 end cell end table
    • Taking square root of both sides we get,
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a equals square root of 73.96 end root end cell row cell a equals 8.6 end cell end table
    • Therefore, the volume of the given cube is
    Volume = a3 = (8.6)3
    Volume = 636.056 cm3
    • The approximate of the volume is 6.4 from the given options,
    • Therefore the correct option is d) 6.4.
    parallel

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