Maths-
General
Easy
Question
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
- 16016 cm3
- 1616 cm3
- 6016 cm3
- 61160 cm3
Hint:
Volume of frustum of cone = 
The correct answer is: 16016 cm3
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 cm3
Therefore, the correct option is a)16016 cm3
Related Questions to study
Maths-
Given LSA of a cuboid is 900cm2 and the breadth x length are 10cm x 20cm.Calculate height of cuboid.
- We have given,
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 900cm2 and the breadth x length are 10cm x 20cm.Calculate height of cuboid.
Maths-General
- We have given,
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.
factorize the given expressionAns:-
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.
factorize the given expressionAns:-
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 180cm2 and volume is 900cm2
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,
Base area of cuboid = length × breadth = 180 cm²
Volume of cuboid = length × breadth × height = 900 cm³
900 cm³ = 180 cm² × height
= 5 cm
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
Base area of cuboid = length × breadth = 180 cm²
Volume of cuboid = length × breadth × height = 900 cm³
- We will get,
900 cm³ = 180 cm² × height
- On dividing both sides by 180 we get,
= 5 cmThus, 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 180cm2 and volume is 900cm2
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,
Base area of cuboid = length × breadth = 180 cm²
Volume of cuboid = length × breadth × height = 900 cm³
900 cm³ = 180 cm² × height
= 5 cm
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
Base area of cuboid = length × breadth = 180 cm²
Volume of cuboid = length × breadth × height = 900 cm³
- We will get,
900 cm³ = 180 cm² × height
- On dividing both sides by 180 we get,
= 5 cmThus, 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 = (
)πr2h
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 = ()πr2h
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
)πr2hSolution :- 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 = (
)πr2h84π = (
) 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 = ()πr2h
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 = ()πr2h
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
)πr2hSolution :- 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 = (
)πr2h84π = (
) 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.
factorize the given expressionAns:- 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.
factorize the given expressionAns:- 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 cmHeight, 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 cmHeight, 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.
factorize the given expressionAns:- 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.
factorize the given expressionAns:- 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.
Maths-
Dimensions of a rectangular box are 20mx5mx6m,find the difference between T.S.A and L.S.A
- Step 1:We have given area of one face of the cube.
- Step 2: For total surface area, find out the product of the square of side length by 6.
= 6 (81)
= 486
- Step 4: Therefore, the surface of the given cube is 486.
- Therefore, the correct answer is option A) 486 .
Dimensions of a rectangular box are 20mx5mx6m,find the difference between T.S.A and L.S.A
Maths-General
- Step 1:We have given area of one face of the cube.
- Step 2: For total surface area, find out the product of the square of side length by 6.
= 6 (81)
= 486
- Step 4: Therefore, the surface of the given cube is 486.
- Therefore, the correct answer is option A) 486 .
Maths-
A funnel is in the shape of a right circular cone with a base radius of 3 cm and a height of 4 cm. Find the slant height of the funnel
Hint:- Slant height L = 
where h is height
r is radius of base of cone
Solution:- We have given the dimensions of funnel in the shape of cone
Radius, r = 3 cm
Height, h = 4 cm
Let us find the slant height
L =
L =
=
=
L = 5 cm
Therefore, the correct option is b) 5 cm.
where h is height
r is radius of base of cone
Solution:- We have given the dimensions of funnel in the shape of cone
Radius, r = 3 cm
Height, h = 4 cm
Let us find the slant height
L =
L =
=
=
L = 5 cm
Therefore, the correct option is b) 5 cm.
A funnel is in the shape of a right circular cone with a base radius of 3 cm and a height of 4 cm. Find the slant height of the funnel
Maths-General
Hint:- Slant height L =
where h is height
r is radius of base of cone
Solution:- We have given the dimensions of funnel in the shape of cone
Radius, r = 3 cm
Height, h = 4 cm
Let us find the slant height
L =
L =
=
=
L = 5 cm
Therefore, the correct option is b) 5 cm.
where h is height
r is radius of base of cone
Solution:- We have given the dimensions of funnel in the shape of cone
Radius, r = 3 cm
Height, h = 4 cm
Let us find the slant height
L =
L =
=
=
L = 5 cm
Therefore, the correct option is b) 5 cm.
Maths-
Factor the polynomial as the product of binomials.
Ans :- 
is the required product of binomials.
Given ,
Write
As
Here a = x and b =
is the required product of binomials.Given ,
Write
As
Here a = x and b =
∴ is the required product of binomials.
Factor the polynomial as the product of binomials.
Maths-General
Ans :- is the required product of binomials.
Given ,
Write
As
Here a = x and b =
is the required product of binomials.Given ,
Write
As
Here a = x and b =
∴ is the required product of binomials.
Maths-
A triangle having sides equal to 7cm, 24cm and 25cm forms a cone when revolved about 24cm side. What is the volume of a cone formed?
We have given the dimensions of triangle having sides equal to 7cm, 24cm and 25cm
It is revolved about 24 cm side
Therefore, the cone formed will have dimensions as
Height , h = 24 cm
Radius , r = 7 cm
So, the volume of cone = ()πr2h
It is revolved about 24 cm side
Therefore, the cone formed will have dimensions as
Height , h = 24 cm
Radius , r = 7 cm
So, the volume of cone = (
)πr2h= ()(
)(7 x 7)(24)
= 22 x 7 x 8
= 1232 cm3
Therefore, the correct option is b) 1232 cm3
A triangle having sides equal to 7cm, 24cm and 25cm forms a cone when revolved about 24cm side. What is the volume of a cone formed?
Maths-General
We have given the dimensions of triangle having sides equal to 7cm, 24cm and 25cm
It is revolved about 24 cm side
Therefore, the cone formed will have dimensions as
Height , h = 24 cm
Radius , r = 7 cm
So, the volume of cone = ()πr2h
It is revolved about 24 cm side
Therefore, the cone formed will have dimensions as
Height , h = 24 cm
Radius , r = 7 cm
So, the volume of cone = (
)πr2h= ()()(7 x 7)(24)
= 22 x 7 x 8
= 1232 cm3
Therefore, the correct option is b) 1232 cm3
Maths-
What is the factored form of 
Hint :- factorize the given expression by taking out common elements and also using the required formulas .
Ans:- 4x(x+3)(x+3) is the factorized form of the given expression.
Explanation :-
Given,
Taking out common factor 4 we get
Taking out common element x we get
Splitting out 6x into 3x+3x we get
Taking out x+3 common out we get
As we get
∴ 4x (x + 3)(x + 3) is the factorized form of the given expression.
Ans:- 4x(x+3)(x+3) is the factorized form of the given expression.
Explanation :-
Given,
Taking out common factor 4 we get
Taking out common element x we get
Splitting out 6x into 3x+3x we get
Taking out x+3 common out we get
As we get
∴ 4x (x + 3)(x + 3) is the factorized form of the given expression.
What is the factored form of
Maths-General
Hint :- factorize the given expression by taking out common elements and also using the required formulas .
Ans:- 4x(x+3)(x+3) is the factorized form of the given expression.
Explanation :-
Given,
Taking out common factor 4 we get
Taking out common element x we get
Splitting out 6x into 3x+3x we get
Taking out x+3 common out we get
As we get
∴ 4x (x + 3)(x + 3) is the factorized form of the given expression.
Ans:- 4x(x+3)(x+3) is the factorized form of the given expression.
Explanation :-
Given,
Taking out common factor 4 we get
Taking out common element x we get
Splitting out 6x into 3x+3x we get
Taking out x+3 common out we get
As we get
∴ 4x (x + 3)(x + 3) is the factorized form of the given expression.
Maths-
If the area of 1 face is 81 how much is the surface area of the whole cube?
- Step 1:We have given area of one face of the cube.
- Step 2: For total surface area, find out the product of the square of side length by 6.
= 6 (81)
= 486
- Step 4: Therefore, the surface of the given cube is 486.
- Therefore, the correct answer is option A) 486 .
If the area of 1 face is 81 how much is the surface area of the whole cube?
Maths-General
- Step 1:We have given area of one face of the cube.
- Step 2: For total surface area, find out the product of the square of side length by 6.
= 6 (81)
= 486
- Step 4: Therefore, the surface of the given cube is 486.
- Therefore, the correct answer is option A) 486 .
Maths-
calculate the surface area of a cube with a side of 4 mm
- Step 1:We have given the length of the side of the cube.
Side = 4 mm
- Step 2: Find the square of the length of the side of the cube.
- Step 3: For total surface area, find out the product of the square of side length by 6.
= 6(16)
= 96 mm2
- Step 4: Therefore, the surface area of the given cube is 96 mm2.
- Therefore, the correct answer is option B) 96 mm2.
calculate the surface area of a cube with a side of 4 mm
Maths-General
- Step 1:We have given the length of the side of the cube.
Side = 4 mm
- Step 2: Find the square of the length of the side of the cube.
- Step 3: For total surface area, find out the product of the square of side length by 6.
= 6(16)
= 96 mm2
- Step 4: Therefore, the surface area of the given cube is 96 mm2.
- Therefore, the correct answer is option B) 96 mm2.
Maths-
Ratio of volume of a cone to the volume of a cylinder for same base radius and
same height is __________
Solution :- Here is the activity for finding the volume of cone
Let us take a cylinder of height "h", base radius "r", and take 3 cones of height "h". Fill the cones with water and empty out one cone at a time
Each cone fills the cylinder to one-third quantity. Hence, such three cones will fill the cylinder. Thus, the volume of a cone is one-third of the volume of the cylinder.
Volume of cone = (1/3) × Volume of cylinder
= () × πr2h
= ()πr2h
So the ratio of volume of cone to the volume of cylinder is 1:3
Therefore , the correct option is b) 1:3
Let us take a cylinder of height "h", base radius "r", and take 3 cones of height "h". Fill the cones with water and empty out one cone at a time
Each cone fills the cylinder to one-third quantity. Hence, such three cones will fill the cylinder. Thus, the volume of a cone is one-third of the volume of the cylinder.
Volume of cone = (1/3) × Volume of cylinder
= (
) × πr2h= (
)πr2hSo the ratio of volume of cone to the volume of cylinder is 1:3
Therefore , the correct option is b) 1:3
Ratio of volume of a cone to the volume of a cylinder for same base radius and
same height is __________
Maths-General
Solution :- Here is the activity for finding the volume of cone
Let us take a cylinder of height "h", base radius "r", and take 3 cones of height "h". Fill the cones with water and empty out one cone at a time
Each cone fills the cylinder to one-third quantity. Hence, such three cones will fill the cylinder. Thus, the volume of a cone is one-third of the volume of the cylinder.
Volume of cone = (1/3) × Volume of cylinder
= () × πr2h
= ()πr2h
So the ratio of volume of cone to the volume of cylinder is 1:3
Therefore , the correct option is b) 1:3
Let us take a cylinder of height "h", base radius "r", and take 3 cones of height "h". Fill the cones with water and empty out one cone at a time
Each cone fills the cylinder to one-third quantity. Hence, such three cones will fill the cylinder. Thus, the volume of a cone is one-third of the volume of the cylinder.
Volume of cone = (1/3) × Volume of cylinder
= (
) × πr2h= (
)πr2hSo the ratio of volume of cone to the volume of cylinder is 1:3
Therefore , the correct option is b) 1:3
