# Mensuration Questions and Answers updated daily – Aptitude

Mensuration Questions: Solved 782 Mensuration Questions and answers section with explanation for various online exam preparation, various interviews, Aptitude Category online test. Category Questions section with detailed description, explanation will help you to master the topic.

## Mensuration Questions

761. Find the curved surface area of a cylinder of length 7 m and a base of radius 3 meter.

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Correct Ans:132

Explanation:

**Solutions:**

Let r and h be the radius and height of the cylinder respectively

Given r = 3 m

h = 7 m

**Curved Surface Area of Cylinder = 2rh**

= 2 * ( 22 / 7 ) * 3 * 7

= 2 * 22 * 3

=

**132 m**

^{2}**Answer is 132**

Workspace

762. The diagonals of rhombus are 18cm and 12 cm. Find the area of the rhombus

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Correct Ans:96 sq. cm

Explanation:

**Solution:**

If d1 and d2 are the diagonals of the

**rhombus**

**Area of the rhombus = ( d1 x d2 ) / 2**

Area = ( 18 x 12 ) / 2

= 216 / 2

=

**108sq cm**

Workspace

763. Find the length of the diagonal of a cuboid 12m long, 9 m broad and 8 m high.

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Correct Ans:17

Explanation:

**Solution is:**

Let l, b and h be the length, breadth and height of the cuboid respectively.

**Diagonal of cuboid =**

=

=

**=**

**=**

**Diagonal of cuboid = 17**

Workspace

764. Find the volume of the cylinder which has a height of 14 meters and a base of radius 3 meters.

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Correct Ans:396

Explanation:

**Solution is**

Let r and h be the radius and height of the cylinders

r = 3 m

h = 14 m

**Volume of cylinder = r**

^{2}h= ( 22 / 7 ) x 3 * 3 * 14

= 22 x 3 x 3 x 2

= 396 m

^{3}

**Answer is 396**

Workspace

765. A coffee grower is going to package his coffee in cylindrical cans which will hold exactly 785 cubic inches of his product. If the cans are to be 10 inches in height, what must be the radius of the can ? (take pi = 3.14)

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Correct Ans:5

Explanation:

**Solution is**

Given ,

Can is in

**Cylindrical**shape

Cylindrical cans hold = Volume of Cylinder

=785 cu.inches

Height of can, h = 10 inches

To find radius of the can :

Volume of cylinder =r

^{2}h = 785

=> ( 3.14 ) r

^{2}x 10 = 785

=> r

^{2}x 31.4 = 785

=> r

^{2}= 785 / 31.4

=> r

^{2}= 25

=> r =

=> r =

**5 inches**

The radius of the can must be

**5 inches**

Workspace

766. Find the area of the parallelogram whose length and breadth are 12 and 15 cm respectively.

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Correct Ans:180 sq cm

Explanation:

**Solution is**

**Area of the paralleogram = l x b**

Area = 12 x 15

= 180 sq cm

**Answer is 180**

Workspace

767. Area of the base of a cuboid 21 sq m, area of side face and other side face are 24 sq m and 14 sq m respectively. Find the volume of the cuboid

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Correct Ans:84

Explanation:

**Solution is**

Let l, b and h be the length, breadth and height of the cuboid respectively.

Given , Area of the base of cuboid = 21 m

^{2}

=> l x b = 21

Given , Area of side face of cuboid = 24 m

^{2}

=> b x h = 24

Given , Area of other side face of cuboid = 14 m

^{2}

=> h x l = 14

**Volume of cuboid = l x b x h cu.unit**

On multiplying equations

We get lxb x bxh x lxh = 21 x 24 x 14

=>l

^{2}x b

^{2}x h

^{2 }= 21 x 24 x 14

=>(l x b x h )

^{2 }=

=

= 7 x 3 x 2 x 2

=

**84**

**Volume of cuboid =l x b x h = 84 cm**

^{3}
Workspace

768. A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is

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Correct Ans:1200

Explanation:

**Solution is**

Let , A hall is in the shape of cuboid as follows

Given l = 15 m

b = 12 m

Area of the floor [ since floor is in rectangular shape, we use area of rectangle ]

= l x b

= 15 x 12

Area of ceiling [ since ceiling is in rectangular shape, we use area of rectangle ]

= l x b

= 15 x 12

Sum of the Areas of four walls = 2 ( l + b ) * h

= 2 ( 15 + 12 ) * h

= 2 ( 27 ) * h

= 54 * h

Given ,

**Ceiling of four walls = Area of the floor + Area of the sum of areas of four walls**

=> ( 15 x 2 ) + ( 15 x 2 ) = 54 * h

=>2 ( 15 x 12 ) = 54 * h

=> 2 ( 180 ) = 54 * h

=> 360 = 54 * h

=> 360 / 54 = h

Volume of the hall = Volume of cuboid

= l x b x h

= 15 x 12 x ( 20 / 3)

= 5 x 12 x 20

**= 1200 m**

^{3}**Answer is 1200**

Workspace

769. Area of the base of a cuboid 9 sq m, area of side face and other side face are 16 sq m and 25 sq m respectively. Find the volume of the cuboid

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Correct Ans:60

Explanation:

**Solution is :**

Let l, b and h be the length, breadth and height of the cuboid respectively.

Given , Area of the base of cuboid = 9 sq.cm

=> l x b = 9

Given , Area of side face of cuboid = 16 m

^{2}

=> b x h = 16

Given , Area of other side face of cuboid = 25 m

^{2}

=> h x l = 25

**Volume of cuboid =**

**l x b x h cu.unit**

On multipliying equations

We get lxb x bxh x lxh= 9 x 16 x 25

=> l

^{2}x b

^{2}x h

^{2}= 9 x 16 x 25

=> (l x b x h )

^{2}=9 x 16 x 25

=> l x b x h =

= 3 x 4 x 5

=

**60**

**Volume of cuboid = l x b x h = 60 m**

^{3}
Workspace

770. Find the length of the diagonal of a cuboid 12m long, 9 m broad and 8 m high.

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Correct Ans:17

Explanation:

**Solution is**

Let l, b and h be the length, breadth and height of the cuboid respectively.

**Diagonal of a cuboid =**

=

=

=

**Diagonal**=

**17**

**Answer is 17**

Workspace

771. A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is ?

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Correct Ans:49

Explanation:

**Solution is**

Let l = 6 m

b = 4 m

h = 1m

**25 cm**

1 m = 100 cm

1 cm = 1 / 100 m

25 cm = 25 / 100

= 1/ 4 m

= 0.25 m

1 m = 100 cm

1 cm = 1 / 100 m

25 cm = 25 / 100

= 1/ 4 m

= 0.25 m

= 1m +

**0.25 cm**

= 1.25 m

**Area of the wet surface = 2 (lb+bh+lh)-lb**

**=2 x ( bh + lh ) + lb**

= 2 x ( 4 x 1.25 + 6 x 1.25) + 6 x 4

= 2 x (5 + 7.5) + 24

= 2 x ( 12.5 ) + 24

= 25 + 24

=

**49**

**Answer is 49**

Workspace

772. Find the area of the square whose diagonal is 8m long

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Correct Ans:32

Explanation:

**Solution is**

**Area of the square = ( diagonal )**

^{2}/ 2In this case, Area of the square = ( 8

^{2 })/ 2

Area = (8 x 8 ) / 2

= 64 / 2

=

**32 sq m**

Answer is 32

Answer is 32

Workspace

773. Area of the base of a cuboid 9 sq m, area of side face and other side face are 16 sq m and 25 sq m respectively. Find the volume of the cuboid

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Correct Ans:60

Explanation:

**Solution is :**

Let l, b and h be the length, breadth and height of the cuboid respectively.

l x b = 9 ,

b x h = 16

and h x l = 25 Mul.

The above equations we get l x b x b x h x l x h = 9 x 16 x 25 (l x b x h)

^{2}

= 9 x 16 x 25 l x b x h

= 3 x 4 x 5 =

**60**

Workspace

774. The diagonals of rhombus are 12cm and 5 cm. Find the area of the rhombus

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Correct Ans:30 sq cm

Explanation:

**Solution is**

If d1 and d2 are the diagonals of the rhombus

then

**Area of the rhombus = (d1 x d2) / 2**

Area = (12 x 5) / 2

= 60 / 2

=

**30 sq cm**

Answer is 30

Answer is 30

Workspace

775. Find the volume of a cuboid with dimension 22 cm by 12 cm by 7.5 cm

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Correct Ans:1980

Explanation:

**Solution is**

Given

Given

Length of the cuboid be l = 22cm

breadth of the cuboid be b = 12cm

height of the cuboid be h = 7.5cm

**Volume of the cuboid is**

**V = l x b x h**

V = 22 x 12 x 7.5 = 1980 cu cm

**Answer is1980**

Workspace

776. Find the volume of a cuboid with dimension 22 cm by 12 cm by 7.5 cm

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Correct Ans:1980

Explanation:

**Solution is**

Given

Given

Length of the cuboid be l = 22cm

breadth of the cuboid be b = 12cm

height of the cuboid be h = 7.5cm

**Volume of the cuboid is**

**V = l x b x h**

V = 22 x 12 x 7.5 = 1980 cu cm

**Answer is1980**

Workspace

777. Find the area of the equilaterla triangle whose sides measure 12 cm

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Correct Ans:36 sqrt(3)

Explanation:

We know that ix x is the side of equilateral triangle,
then area = sqrt(3) . (x^2) / 4
Area = sqrt(3) x 12 x 12 /4 = 36 sqrt(3)

Workspace

778. Find the area of the rectangle having length 24 cm and breadth 21 cm.

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Correct Ans:504

Explanation:

**Solution is**

Given

Given

Length of the rectangle, l = 24 cm

Breadth of the rectangle, b= 21 cm

**Area of the rectangle is**

**A = l x b**

A = 24 x 21 sq cm

A = 504 sqcm

**Answer is504**

Workspace

779. Find the area of the square whose diagonal is 4.2 m long

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Correct Ans:8.82

Explanation:

Area of the square = (diagonal)^2 / 2
In this case, Area of the square = 4.2^2 /2
Area = (4.2 x 4.2 ) /2 = 17.64 / 2 = 8.82 sq m

Workspace

780. Area of the base of a cuboid 49 sq m, area of side face and other side face are 64 sq m and 25 sq m respectively. Find the volume of the cuboid

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Correct Ans:504

Explanation:

**Given**

Let l, b and h be the length, breadth and height of the cuboid respectively

Area of the base =

**l x b = 49 ---> (1)**

Area of side face =

**b x h = 64 ----> (2)**

Area of other side face =

**h x l = 25 ----> (3)**

On multiplying equations (1), (2) and (3), we get

l x b x b x h x l x h = 49 x 64 x 25

=> (l x b x h)^2 = 49 x 64 x 25

=> (l x b x h) = sqrt(49 x 64 x 25)

=> l x b x h = 7 x 8 x 5

= 280

Volume of cuboid = l x b x h = 280

Answer is 280

Workspace

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