Maths-

General

Easy

Question

# Surface area of a cube is 443.76 cm^{2} . Find the volume of it?

- 7.6
- 8.4
- 8.6
- 6.4

Hint:

### Volume of a cube = (side)3 [cubic units]

Total Surface Area(TSA) of cube = 6a2

Where, a is side of cube

## The correct answer is: 6.4

- We are given that

Surface area of a cube = 443.76 cm^{2}

- We have to find volume of the cube

6a^{2 }= 443.76

- Divide both sides of equation by 6

- Taking square root of both sides we get,

- Therefore, the volume of the given cube is

Volume = a^{3} = (8.6)^{3}

Volume = 636.056 cm^{3}

- The approximate of the volume is 6.4 from the given options,
- Therefore the correct option is d) 6.4.

### Related Questions to study

Maths-

### Find the volume of the cone. Round decimals nearest tenth r = 14ft, h = 18 ft

Hint:- Volume of a cone = ()πr

Solution :- We have given the dimensions of a cone

Radius , r = 14 ft

Height , h = 18 ft

We have to find the volume of the given cone

We know that

Volume of a cone = ()πr

= ()(3.14)(14 x 14)(18)

= ()(3.14) (196 x 18)

= ()(3.14)(3528)

= 11077.9 / 3

= 3692.6 ft

Therefore correct option is b) 3692.6 ft

^{2}hSolution :- We have given the dimensions of a cone

Radius , r = 14 ft

Height , h = 18 ft

We have to find the volume of the given cone

We know that

Volume of a cone = ()πr

^{2}h= ()(3.14)(14 x 14)(18)

= ()(3.14) (196 x 18)

= ()(3.14)(3528)

= 11077.9 / 3

= 3692.6 ft

^{3}Therefore correct option is b) 3692.6 ft

^{3}.### Find the volume of the cone. Round decimals nearest tenth r = 14ft, h = 18 ft

Maths-General

Hint:- Volume of a cone = ()πr

Solution :- We have given the dimensions of a cone

Radius , r = 14 ft

Height , h = 18 ft

We have to find the volume of the given cone

We know that

Volume of a cone = ()πr

= ()(3.14)(14 x 14)(18)

= ()(3.14) (196 x 18)

= ()(3.14)(3528)

= 11077.9 / 3

= 3692.6 ft

Therefore correct option is b) 3692.6 ft

^{2}hSolution :- We have given the dimensions of a cone

Radius , r = 14 ft

Height , h = 18 ft

We have to find the volume of the given cone

We know that

Volume of a cone = ()πr

^{2}h= ()(3.14)(14 x 14)(18)

= ()(3.14) (196 x 18)

= ()(3.14)(3528)

= 11077.9 / 3

= 3692.6 ft

^{3}Therefore correct option is b) 3692.6 ft

^{3}.Maths-

### The dimensions of a cuboid are in the ratio of 4:3:2 and its total surface area is 1300 cm^{2 }. Find its length, breadth, and height respectively?

Given: Ratio of dimensions of a cuboid is 4:3:2 & The Total surface area of cuboid is 1300 cm².

We have to find Length, breadth & height of cuboid.

where, l, b & h are length, breadth and height of cuboid respectively.

Height, h = 2x

TSA = 1300 cm

Therefore,

The dimensions of cuboid are,

Length = 4x = 4(5)= 20

Breadth= 3x = 3(5) =15

Height = 2x=2(5)= 10

Thus, The length, breadth & height of cuboid are 20 cm, 15 cm & 10 cm respectively.

Therefore the correct option is d) 20 cm,15cm , 10 cm

We have to find Length, breadth & height of cuboid.

- Let length, breadth and height of cuboid be 4x, 3x and 2x respectively.⠀⠀

- Now, As we know that, total surface area of cuboid is given by,

where, l, b & h are length, breadth and height of cuboid respectively.

- We have , length = 4x

Height, h = 2x

TSA = 1300 cm

^{2}- Putting the values in the formula

- Dividing both sides of equation by 2

- Dividing both sides of equation by 26

Therefore,

The dimensions of cuboid are,

Length = 4x = 4(5)= 20

Breadth= 3x = 3(5) =15

Height = 2x=2(5)= 10

Thus, The length, breadth & height of cuboid are 20 cm, 15 cm & 10 cm respectively.

Therefore the correct option is d) 20 cm,15cm , 10 cm

### The dimensions of a cuboid are in the ratio of 4:3:2 and its total surface area is 1300 cm^{2 }. Find its length, breadth, and height respectively?

Maths-General

Given: Ratio of dimensions of a cuboid is 4:3:2 & The Total surface area of cuboid is 1300 cm².

We have to find Length, breadth & height of cuboid.

where, l, b & h are length, breadth and height of cuboid respectively.

Height, h = 2x

TSA = 1300 cm

Therefore,

The dimensions of cuboid are,

Length = 4x = 4(5)= 20

Breadth= 3x = 3(5) =15

Height = 2x=2(5)= 10

Thus, The length, breadth & height of cuboid are 20 cm, 15 cm & 10 cm respectively.

Therefore the correct option is d) 20 cm,15cm , 10 cm

We have to find Length, breadth & height of cuboid.

- Let length, breadth and height of cuboid be 4x, 3x and 2x respectively.⠀⠀

- Now, As we know that, total surface area of cuboid is given by,

where, l, b & h are length, breadth and height of cuboid respectively.

- We have , length = 4x

Height, h = 2x

TSA = 1300 cm

^{2}- Putting the values in the formula

- Dividing both sides of equation by 2

- Dividing both sides of equation by 26

Therefore,

The dimensions of cuboid are,

Length = 4x = 4(5)= 20

Breadth= 3x = 3(5) =15

Height = 2x=2(5)= 10

Thus, The length, breadth & height of cuboid are 20 cm, 15 cm & 10 cm respectively.

Therefore the correct option is d) 20 cm,15cm , 10 cm

Maths-

### Find the volume of the cone. Round decimals nearest tenth. D = 12cm, h = 8 cm

Hint:- Volume of a cone = ()πr

Solution :- We have given the dimensions of a cone

Diameter = 12 cm

Radius, r = = 6 cm

Height, h = 8 cm

We have to find the volume of the given cone

We know that

Volume of a cone = ()πr

= ()(3.14)(6 x 6) (8)

= ()(3.14) (36 x 8)

= ()(3.14)(288)

= 904.

= 301.4 cm

Therefore correct option is c) 301.4 cm

^{2}hSolution :- We have given the dimensions of a cone

Diameter = 12 cm

Radius, r = = 6 cm

Height, h = 8 cm

We have to find the volume of the given cone

We know that

Volume of a cone = ()πr

^{2}h= ()(3.14)(6 x 6) (8)

= ()(3.14) (36 x 8)

= ()(3.14)(288)

= 904.

= 301.4 cm

^{3}Therefore correct option is c) 301.4 cm

^{3}.### Find the volume of the cone. Round decimals nearest tenth. D = 12cm, h = 8 cm

Maths-General

Hint:- Volume of a cone = ()πr

Solution :- We have given the dimensions of a cone

Diameter = 12 cm

Radius, r = = 6 cm

Height, h = 8 cm

We have to find the volume of the given cone

We know that

Volume of a cone = ()πr

= ()(3.14)(6 x 6) (8)

= ()(3.14) (36 x 8)

= ()(3.14)(288)

= 904.

= 301.4 cm

Therefore correct option is c) 301.4 cm

^{2}hSolution :- We have given the dimensions of a cone

Diameter = 12 cm

Radius, r = = 6 cm

Height, h = 8 cm

We have to find the volume of the given cone

We know that

Volume of a cone = ()πr

^{2}h= ()(3.14)(6 x 6) (8)

= ()(3.14) (36 x 8)

= ()(3.14)(288)

= 904.

= 301.4 cm

^{3}Therefore correct option is c) 301.4 cm

^{3}.Maths-

Hint :- Divide the mid term as a product of 1st and 3rd elements and take common elements out.

Ans:- Option B

Explanation:-

Given,

Divide -2ab into -ab and -ab so that (-ab)(-ab) = we get

Taking common elements we get

Taking (a-b) common gives

∴ Option B is correct

Ans:- Option B

Explanation:-

Given,

Divide -2ab into -ab and -ab so that (-ab)(-ab) = we get

Taking common elements we get

Taking (a-b) common gives

∴ Option B is correct

Maths-General

Hint :- Divide the mid term as a product of 1st and 3rd elements and take common elements out.

Ans:- Option B

Explanation:-

Given,

Divide -2ab into -ab and -ab so that (-ab)(-ab) = we get

Taking common elements we get

Taking (a-b) common gives

∴ Option B is correct

Ans:- Option B

Explanation:-

Given,

Divide -2ab into -ab and -ab so that (-ab)(-ab) = we get

Taking common elements we get

Taking (a-b) common gives

∴ Option B is correct

Maths-

### Find out the side of cube if the complete surface area is given to be 346.56 cm^{2}.

- Step 1:We have given the total surface area of the cube.

^{2}

- Step 2: We know that

^{2}

346.56 = 6a

^{2}

^{· }Step 3: For finding the side firstly divide both sides if equation by 6

- Step 4:- Taking square root of both sides we get,

^{· }Step 5: Therefore, the length of side of the given cube is 7.6 cm^{2}.- Therefore, the correct answer is option B) 7.6 cm.

### Find out the side of cube if the complete surface area is given to be 346.56 cm^{2}.

Maths-General

- Step 1:We have given the total surface area of the cube.

^{2}

- Step 2: We know that

^{2}

346.56 = 6a

^{2}

^{· }Step 3: For finding the side firstly divide both sides if equation by 6

- Step 4:- Taking square root of both sides we get,

^{· }Step 5: Therefore, the length of side of the given cube is 7.6 cm^{2}.- Therefore, the correct answer is option B) 7.6 cm.

Maths-

### Find the volume of the cone. Use 3.14 for π. Round decimal answers to the nearest tenth. r= 4 in, height = 4 in

Hint:- Volume of a cone = ()πr

Solution :- We have given the dimensions of a cone

Radius, r = 4 in

Height, h = 4 in

We have to find the volume of the given cone

We know that

Volume of a cone = ()πr

= ()(3.14)(4 x 4) (4)

= ()(3.14) (16 x 4)

= ()(3.14)(64)

= 200.

= 66.9 in

Therefore correct option is b) 66.9 in

^{2}hSolution :- We have given the dimensions of a cone

Radius, r = 4 in

Height, h = 4 in

We have to find the volume of the given cone

We know that

Volume of a cone = ()πr

^{2}h= ()(3.14)(4 x 4) (4)

= ()(3.14) (16 x 4)

= ()(3.14)(64)

= 200.

= 66.9 in

^{3}Therefore correct option is b) 66.9 in

^{3}.### Find the volume of the cone. Use 3.14 for π. Round decimal answers to the nearest tenth. r= 4 in, height = 4 in

Maths-General

Hint:- Volume of a cone = ()πr

Solution :- We have given the dimensions of a cone

Radius, r = 4 in

Height, h = 4 in

We have to find the volume of the given cone

We know that

Volume of a cone = ()πr

= ()(3.14)(4 x 4) (4)

= ()(3.14) (16 x 4)

= ()(3.14)(64)

= 200.

= 66.9 in

Therefore correct option is b) 66.9 in

^{2}hSolution :- We have given the dimensions of a cone

Radius, r = 4 in

Height, h = 4 in

We have to find the volume of the given cone

We know that

Volume of a cone = ()πr

^{2}h= ()(3.14)(4 x 4) (4)

= ()(3.14) (16 x 4)

= ()(3.14)(64)

= 200.

= 66.9 in

^{3}Therefore correct option is b) 66.9 in

^{3}.Maths-

### Calculate the LSA of a cuboid of ,length = 40cm ,breadth = 20cm and height = 10cm.

- We are given the dimensions of cuboid.

breadth = 20cm = b

height = 10cm = h

- We will calculate the LSA of given cuboid

The Lateral Surface area of cuboid = 2h( l + b)

- By using the above formula of the lateral surface area of the cuboid, we get

= 2h( l + b)

= 2 10 (40 + 20)

= 20 (60)

LSA= 1200 cm^{2}

Therefore the Lateral surface area of the given cuboid is 1200 cm^{2}.

The correct answer is option d) 1200.

### Calculate the LSA of a cuboid of ,length = 40cm ,breadth = 20cm and height = 10cm.

Maths-General

- We are given the dimensions of cuboid.

breadth = 20cm = b

height = 10cm = h

- We will calculate the LSA of given cuboid

The Lateral Surface area of cuboid = 2h( l + b)

- By using the above formula of the lateral surface area of the cuboid, we get

= 2h( l + b)

= 2 10 (40 + 20)

= 20 (60)

LSA= 1200 cm^{2}

Therefore the Lateral surface area of the given cuboid is 1200 cm^{2}.

The correct answer is option d) 1200.

Maths-

### The diameter of the ends of a bucket of height 24 cm are 42 cm and 14 cm

respectively .Find the capacity of the bucket

Hint:- Volume of frustum of cone =

Solution:- We have given the dimensions of a bucket which is of frustrum shape

Top diameter = 42 cm

Top radius, R = 21 cm

Bottom diameter = 14

Bottom radius, r = 7 cm

Height of frustrum , h = 24 cm

Therefore capacity of bucket = volume of bucket

=

=

=

= 176 × 91

=

Therefore, the correct option is a)16016 cm

Solution:- We have given the dimensions of a bucket which is of frustrum shape

Top diameter = 42 cm

Top radius, R = 21 cm

Bottom diameter = 14

Bottom radius, r = 7 cm

Height of frustrum , h = 24 cm

Therefore capacity of bucket = volume of bucket

=

=

=

= 176 × 91

=

Therefore, the correct option is a)16016 cm

^{3}### The diameter of the ends of a bucket of height 24 cm are 42 cm and 14 cm

respectively .Find the capacity of the bucket

Maths-General

Hint:- Volume of frustum of cone =

Solution:- We have given the dimensions of a bucket which is of frustrum shape

Top diameter = 42 cm

Top radius, R = 21 cm

Bottom diameter = 14

Bottom radius, r = 7 cm

Height of frustrum , h = 24 cm

Therefore capacity of bucket = volume of bucket

=

=

=

= 176 × 91

=

Therefore, the correct option is a)16016 cm

Solution:- We have given the dimensions of a bucket which is of frustrum shape

Top diameter = 42 cm

Top radius, R = 21 cm

Bottom diameter = 14

Bottom radius, r = 7 cm

Height of frustrum , h = 24 cm

Therefore capacity of bucket = volume of bucket

=

=

=

= 176 × 91

=

Therefore, the correct option is a)16016 cm

^{3}Maths-

### Given LSA of a cuboid is 900cm^{2 }and the breadth x length are 10cm x 20cm.Calculate height of cuboid.

- We have given,

^{2}

Breadth= 10 cm

Length = 20 cm

- We know that ,

- Insert the values in the above equation.

900 = 2h(30)

Divide both sides of equation by 30, we get

Divide both sides of equation by 2, we get

h = 15

- Therefore the height of given cuboid is 15 cm.
- The correct option is option a) 15 .

### Given LSA of a cuboid is 900cm^{2 }and the breadth x length are 10cm x 20cm.Calculate height of cuboid.

Maths-General

- We have given,

^{2}

Breadth= 10 cm

Length = 20 cm

- We know that ,

- Insert the values in the above equation.

900 = 2h(30)

Divide both sides of equation by 30, we get

Divide both sides of equation by 2, we get

h = 15

- Therefore the height of given cuboid is 15 cm.
- The correct option is option a) 15 .

Maths-

### Factor the given expression completely.

HINT :- using the formula factorize the given expression

Ans:- is the factorized form of the given expression.

Explanation :-

Given,

Taking out common factor -3x out of equation , we get

Write

Applying

Here a = x ; b = 3

We get ,

∴ is the factorized form of the given expression.

Ans:- is the factorized form of the given expression.

Explanation :-

Given,

Taking out common factor -3x out of equation , we get

Write

Applying

Here a = x ; b = 3

We get ,

∴ is the factorized form of the given expression.

### Factor the given expression completely.

Maths-General

HINT :- using the formula factorize the given expression

Ans:- is the factorized form of the given expression.

Explanation :-

Given,

Taking out common factor -3x out of equation , we get

Write

Applying

Here a = x ; b = 3

We get ,

∴ is the factorized form of the given expression.

Ans:- is the factorized form of the given expression.

Explanation :-

Given,

Taking out common factor -3x out of equation , we get

Write

Applying

Here a = x ; b = 3

We get ,

∴ is the factorized form of the given expression.

Maths-

### Find the height of a cuboid whose base area is 180cm^{2} and volume is 900cm^{2}

Volume of cuboid = Base area × Height [Cubic units]

The base of the cuboid is rectangle in shape. So, the base area of a cuboid is equal to the product of its length and breadth. Hence,

Volume of a cuboid = length × breadth × height [cubic units]

or

Volume of a cuboid = l × b × h [cubic units]

Where,

Volume of cuboid = length × breadth × height = 900 cm³

900 cm³ = 180 cm² × height

Thus, the height of the cuboid is 5 cm.

The correct option is c) 5 cm .

The base of the cuboid is rectangle in shape. So, the base area of a cuboid is equal to the product of its length and breadth. Hence,

Volume of a cuboid = length × breadth × height [cubic units]

or

Volume of a cuboid = l × b × h [cubic units]

Where,

- l = length
- b = breadth
- h = height

- We have given that,

Volume of cuboid = length × breadth × height = 900 cm³

- We will get,

900 cm³ = 180 cm² × height

- On dividing both sides by 180 we get,

Thus, the height of the cuboid is 5 cm.

The correct option is c) 5 cm .

### Find the height of a cuboid whose base area is 180cm^{2} and volume is 900cm^{2}

Maths-General

Volume of cuboid = Base area × Height [Cubic units]

The base of the cuboid is rectangle in shape. So, the base area of a cuboid is equal to the product of its length and breadth. Hence,

Volume of a cuboid = length × breadth × height [cubic units]

or

Volume of a cuboid = l × b × h [cubic units]

Where,

Volume of cuboid = length × breadth × height = 900 cm³

900 cm³ = 180 cm² × height

Thus, the height of the cuboid is 5 cm.

The correct option is c) 5 cm .

The base of the cuboid is rectangle in shape. So, the base area of a cuboid is equal to the product of its length and breadth. Hence,

Volume of a cuboid = length × breadth × height [cubic units]

or

Volume of a cuboid = l × b × h [cubic units]

Where,

- l = length
- b = breadth
- h = height

- We have given that,

Volume of cuboid = length × breadth × height = 900 cm³

- We will get,

900 cm³ = 180 cm² × height

- On dividing both sides by 180 we get,

Thus, the height of the cuboid is 5 cm.

The correct option is c) 5 cm .

Maths-

### A cone has a circular base of radius 6m and volume 84π m³. The height of cone is

Hint:- Volume of a cone = ()πr

Solution :- We have given the dimensions of a cone

Radius , r = 6 m

Volume of cone = 84π m³

We have to find the height of the given cone

Let height of the cone be h

We know that

Volume of a cone = ()πr

84π = () π (6 x 6) (h)

Divide both sides of equation by π

84 = (2 x 6) (h)

84 = 12h)

h =

h = 7 m

Therefore correct option is a) 7m

^{2}hSolution :- We have given the dimensions of a cone

Radius , r = 6 m

Volume of cone = 84π m³

We have to find the height of the given cone

Let height of the cone be h

We know that

Volume of a cone = ()πr

^{2}h84π = () π (6 x 6) (h)

Divide both sides of equation by π

84 = (2 x 6) (h)

84 = 12h)

h =

h = 7 m

Therefore correct option is a) 7m

### A cone has a circular base of radius 6m and volume 84π m³. The height of cone is

Maths-General

Hint:- Volume of a cone = ()πr

Solution :- We have given the dimensions of a cone

Radius , r = 6 m

Volume of cone = 84π m³

We have to find the height of the given cone

Let height of the cone be h

We know that

Volume of a cone = ()πr

84π = () π (6 x 6) (h)

Divide both sides of equation by π

84 = (2 x 6) (h)

84 = 12h)

h =

h = 7 m

Therefore correct option is a) 7m

^{2}hSolution :- We have given the dimensions of a cone

Radius , r = 6 m

Volume of cone = 84π m³

We have to find the height of the given cone

Let height of the cone be h

We know that

Volume of a cone = ()πr

^{2}h84π = () π (6 x 6) (h)

Divide both sides of equation by π

84 = (2 x 6) (h)

84 = 12h)

h =

h = 7 m

Therefore correct option is a) 7m

Maths-

### What is the factored form of ?

HINT :- using the formula factorize the given expression

Ans:- 2 (5x + 4)(5x - 4) is the factorized form of the given expression.

Explanation :-

Given,

Taking out common factor 2 out of equation , we get

Write

Applying

We get ,

∴ 2(5x+4y)(5x-4y) is the factorized form of the given expression.

Ans:- 2 (5x + 4)(5x - 4) is the factorized form of the given expression.

Explanation :-

Given,

Taking out common factor 2 out of equation , we get

Write

Applying

We get ,

∴ 2(5x+4y)(5x-4y) is the factorized form of the given expression.

### What is the factored form of ?

Maths-General

HINT :- using the formula factorize the given expression

Ans:- 2 (5x + 4)(5x - 4) is the factorized form of the given expression.

Explanation :-

Given,

Taking out common factor 2 out of equation , we get

Write

Applying

We get ,

∴ 2(5x+4y)(5x-4y) is the factorized form of the given expression.

Ans:- 2 (5x + 4)(5x - 4) is the factorized form of the given expression.

Explanation :-

Given,

Taking out common factor 2 out of equation , we get

Write

Applying

We get ,

∴ 2(5x+4y)(5x-4y) is the factorized form of the given expression.

Maths-

### Find the slant height of the right circular cone if the base diameter of the right circular cone is 14 cm and the height is 24 cm.

Hint:- Slant height L =

where h is height

r is radius of base of cone

Solution:- We have given the dimensions of a right circular cone

Base diameter = 14 cm

Radius, r = = 7 cm

Height, h = 24 cm

Let us find the slant height

L =

L =

=

=

L = 25 cm

Therefore, the correct option is d) 25 cm.

where h is height

r is radius of base of cone

Solution:- We have given the dimensions of a right circular cone

Base diameter = 14 cm

Radius, r = = 7 cm

Height, h = 24 cm

Let us find the slant height

L =

L =

=

=

L = 25 cm

Therefore, the correct option is d) 25 cm.

### Find the slant height of the right circular cone if the base diameter of the right circular cone is 14 cm and the height is 24 cm.

Maths-General

Hint:- Slant height L =

where h is height

r is radius of base of cone

Solution:- We have given the dimensions of a right circular cone

Base diameter = 14 cm

Radius, r = = 7 cm

Height, h = 24 cm

Let us find the slant height

L =

L =

=

=

L = 25 cm

Therefore, the correct option is d) 25 cm.

where h is height

r is radius of base of cone

Solution:- We have given the dimensions of a right circular cone

Base diameter = 14 cm

Radius, r = = 7 cm

Height, h = 24 cm

Let us find the slant height

L =

L =

=

=

L = 25 cm

Therefore, the correct option is d) 25 cm.

Maths-

### Factor the given expression completely.

HINT :- using the formula factorize the given expression

Ans:- 16 (2xy + 3z) (2xy - 3z) is the factorized form of the given expression.

Explanation :-

Given,

Taking out common factor 16 out of equation , we get

Write

Applying

Here a = 2xy ; b = 3z

We get ,

∴ 16 ( 2xy + 3z ) ( 2xy - 3z ) is the factorized form of the given expression.

Ans:- 16 (2xy + 3z) (2xy - 3z) is the factorized form of the given expression.

Explanation :-

Given,

Taking out common factor 16 out of equation , we get

Write

Applying

Here a = 2xy ; b = 3z

We get ,

∴ 16 ( 2xy + 3z ) ( 2xy - 3z ) is the factorized form of the given expression.

### Factor the given expression completely.

Maths-General

HINT :- using the formula factorize the given expression

Ans:- 16 (2xy + 3z) (2xy - 3z) is the factorized form of the given expression.

Explanation :-

Given,

Taking out common factor 16 out of equation , we get

Write

Applying

Here a = 2xy ; b = 3z

We get ,

∴ 16 ( 2xy + 3z ) ( 2xy - 3z ) is the factorized form of the given expression.

Ans:- 16 (2xy + 3z) (2xy - 3z) is the factorized form of the given expression.

Explanation :-

Given,

Taking out common factor 16 out of equation , we get

Write

Applying

Here a = 2xy ; b = 3z

We get ,

∴ 16 ( 2xy + 3z ) ( 2xy - 3z ) is the factorized form of the given expression.