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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 = 2Pirh
= 2 * ( 22 / 7 ) * 3 * 7
= 2 * 22 * 3
= 132 m2
Answer is 132
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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
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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 =sqrt{l^{2} + b^{2} + h^{2}}
=sqrt{12^{2} + 9^{2} + 8^{2} }

=sqrt{144 + 81 + 64}
=sqrt{289}
Diagonal of cuboid = 17
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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 = Pir2h
= ( 22 / 7 ) x 3 * 3 * 14
= 22 x 3 x 3 x 2
= 396 m3
Answer is 396
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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 =Pir2h = 785
=> ( 3.14 ) r2x 10 = 785
=> r2x 31.4 = 785
=> r2= 785 / 31.4
=> r2= 25
=> r =sqrt{25}
=> r =5 inches
The radius of the can must be5 inches
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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
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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 m2
=> l x b = 21
Given , Area of side face of cuboid = 24 m2
=> b x h = 24
Given , Area of other side face of cuboid = 14 m2
=> 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
=>l2x b2x h2 = 21 x 24 x 14
=>(l x b x h )2 =sqrt{21 x 24 x 14}
=sqrt{(7 x 3) x (2 x 2x 2 x 3) x (7 x 2)}
= 7 x 3 x 2 x 2
= 84
Volume of cuboid =l x b x h = 84 cm3

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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 m3
Answer is 1200
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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 m2
=> b x h = 16
Given , Area of other side face of cuboid = 25 m2
=> 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
=> l2 x b2 x h2= 9 x 16 x 25
=> (l x b x h )2 =9 x 16 x 25
=> l x b x h =sqrt{9 x 16 x 25}
= 3 x 4 x 5
= 60
Volume of cuboid = l x b x h = 60 m3
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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 = sqrt{lxl + bxb + hxh}
= sqrt{12 x 12 + 9 x 9 + 8 x 8}
= sqrt{144 + 81 + 64}
= sqrt{289}
Diagonal = 17
Answer is 17
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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 = 1m25 cm
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
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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 / 2
In this case, Area of the square = ( 82 )/ 2
Area = (8 x 8 ) / 2
= 64 / 2
= 32 sq m
Answer is 32
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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
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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
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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

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 isV = l x b x h
V = 22 x 12 x 7.5 = 1980 cu cm
Answer is1980
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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

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 isV = l x b x h
V = 22 x 12 x 7.5 = 1980 cu cm
Answer is1980
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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)
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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

Length of the rectangle, l = 24 cm
Breadth of the rectangle, b= 21 cm
Area of the rectangle isA = l x b
A = 24 x 21 sq cm
A = 504 sqcm
Answer is504
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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
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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
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