Maths-

General

Easy

Question

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

- 9 cm
- 10 cm
- 5 cm
- 3 cm

Hint:

### Volume of cuboid is the total space occupied by the cuboid in a three-dimensional space. A cuboid is a three-dimensional structure having six rectangular faces. These six faces of the cuboid exist as a pair of three parallel faces. Therefore, the volume is a measure based on the dimensions of these faces, i.e. length, width and height. It is measured in cubic units.

## The correct answer is: 5 cm

### 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,

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

We have given that,

Base area of cuboid = length × breadth = 180 cm²

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

- We will get,

Volume of a cuboid = Base area of cuboid × height of the cuboid

900 cm³ = 180 cm² × height

- On dividing both sides by 180 we get,

height = = 5 cm

Thus, the height of the cuboid is 5 cm.

The correct option is c) 5 cm .

### Related Questions to study

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.

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 =

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 =

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 = ()πr

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 = ()πr

^{2}h= ()()(7 x 7)(24)

= 22 x 7 x 8

= 1232 cm^{3}

Therefore, the correct option is b) 1232 cm^{3}

### 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 = ()πr

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 = ()πr

^{2}h= ()()(7 x 7)(24)

= 22 x 7 x 8

= 1232 cm^{3}

Therefore, the correct option is b) 1232 cm^{3}

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.

^{2}= (4)

^{2}= 16 mm

^{2}

- Step 3: For total surface area, find out the product of the square of side length by 6.

^{2}

= 6(16)

= 96 mm^{2}

- Step 4: Therefore, the surface area of the given cube is 96 mm
^{2}. - Therefore, the correct answer is option B) 96 mm
^{2}.

### 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.

^{2}= (4)

^{2}= 16 mm

^{2}

- Step 3: For total surface area, find out the product of the square of side length by 6.

^{2}

= 6(16)

= 96 mm^{2}

- Step 4: Therefore, the surface area of the given cube is 96 mm
^{2}. - Therefore, the correct answer is option B) 96 mm
^{2}.

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

= () × πr

= ()πr

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

= () × πr

^{2}h= ()πr

^{2}hSo 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

= () × πr

= ()πr

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

= () × πr

^{2}h= ()πr

^{2}hSo the ratio of volume of cone to the volume of cylinder is 1:3

Therefore , the correct option is b) 1:3

Maths-

### Find the Total surface area if the given dimensions are 6 cm,4cm, and 5 cm.

Hint:- We have given three different dimensions ,

Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]

where

l → length of the cuboid

b → breadth of the cuboid

h → height of the cuboid

Solution:-

We will calculate the total surface area of a cuboid by using the following formula:

The dimensions of the given cuboid:

Length, l = 4 cm

Breadth, b = 5 cm

Height, h = 6 cm

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

The total surface area of the given cuboid is,

=

=

=

=

= 148 cm

Thus, the total surface area of a cuboid of dimensions 6 cm, 4 cm & 5 cm is 148 cm².

The correct option is C)148 cm².

Note:- In some examples it may be given the surface area and any two dimensions , then we have to adjust the formula such a that we will be able to find out the required value . For eg- If area , length and breadth is given the formula for height becomes

Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]

where

l → length of the cuboid

b → breadth of the cuboid

h → height of the cuboid

Solution:-

We will calculate the total surface area of a cuboid by using the following formula:

Length, l = 4 cm

Breadth, b = 5 cm

Height, h = 6 cm

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

The total surface area of the given cuboid is,

=

=

=

=

= 148 cm

^{2}Thus, the total surface area of a cuboid of dimensions 6 cm, 4 cm & 5 cm is 148 cm².

The correct option is C)148 cm².

Note:- In some examples it may be given the surface area and any two dimensions , then we have to adjust the formula such a that we will be able to find out the required value . For eg- If area , length and breadth is given the formula for height becomes

### Find the Total surface area if the given dimensions are 6 cm,4cm, and 5 cm.

Maths-General

Hint:- We have given three different dimensions ,

Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]

where

l → length of the cuboid

b → breadth of the cuboid

h → height of the cuboid

Solution:-

We will calculate the total surface area of a cuboid by using the following formula:

The dimensions of the given cuboid:

Length, l = 4 cm

Breadth, b = 5 cm

Height, h = 6 cm

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

The total surface area of the given cuboid is,

=

=

=

=

= 148 cm

Thus, the total surface area of a cuboid of dimensions 6 cm, 4 cm & 5 cm is 148 cm².

The correct option is C)148 cm².

Note:- In some examples it may be given the surface area and any two dimensions , then we have to adjust the formula such a that we will be able to find out the required value . For eg- If area , length and breadth is given the formula for height becomes

Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]

where

l → length of the cuboid

b → breadth of the cuboid

h → height of the cuboid

Solution:-

We will calculate the total surface area of a cuboid by using the following formula:

Length, l = 4 cm

Breadth, b = 5 cm

Height, h = 6 cm

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

The total surface area of the given cuboid is,

=

=

=

=

= 148 cm

^{2}Thus, the total surface area of a cuboid of dimensions 6 cm, 4 cm & 5 cm is 148 cm².

The correct option is C)148 cm².

Note:- In some examples it may be given the surface area and any two dimensions , then we have to adjust the formula such a that we will be able to find out the required value . For eg- If area , length and breadth is given the formula for height becomes

Maths-

### Factor the given expression.

ANS :- (3x-10)(3x+10) is the factorized form of the given expression.

Given ,

Using square root and squaring on 9 and 100 . we get

using the formula

Here

Then

∴ (3x - 10) (3x + 10) is the factorized form of the given expression.

Given ,

Using square root and squaring on 9 and 100 . we get

using the formula

Here

Then

∴ (3x - 10) (3x + 10) is the factorized form of the given expression.

### Factor the given expression.

Maths-General

ANS :- (3x-10)(3x+10) is the factorized form of the given expression.

Given ,

Using square root and squaring on 9 and 100 . we get

using the formula

Here

Then

∴ (3x - 10) (3x + 10) is the factorized form of the given expression.

Given ,

Using square root and squaring on 9 and 100 . we get

using the formula

Here

Then

∴ (3x - 10) (3x + 10) is the factorized form of the given expression.

Maths-

### Factor the polynomial as the product of binomials.

Ans :- is the required product of binomials.

Given ,

Write then we get

As

Here a = x and b =

x

∴ (x+)(x+) is the required product of binomials.

Given ,

Write then we get

As

Here a = x and b =

x

^{2 }+ x + = (x +)^{2}= (x + ) (x +)∴ (x+)(x+) 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 then we get

As

Here a = x and b =

x

∴ (x+)(x+) is the required product of binomials.

Given ,

Write then we get

As

Here a = x and b =

x

^{2 }+ x + = (x +)^{2}= (x + ) (x +)∴ (x+)(x+) is the required product of binomials.