Volume and Surface Area- Aptitude Questions and Answers

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If the volume of a cylinder is 2156 cubic cm and height is 14 cm, find its radius?

A)

14 cm


B)

21 cm


C)

3.5 cm


D)

7 cm



Correct Answer :

7 cm


Explanation :

h = 14 cm, r = ?
Volume = 2156 cm3
πr2h = 2156
22/7 * r2 *14 = 2156
r2 = 2156*7 / 22*14
r2 = 49
r = 7 cm

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The volume of a right circular cylinder is 392π cm3 and its height is 8 cm. Find the radius?

A)

6 cm


B)

7 cm


C)

8 cm


D)

9 cm



Correct Answer :

7 cm


Explanation :

Volume of a cylinder = πr2h
392π = π*r2*8
r2 = 392/8
r2 = 49
r = 7 cm

If the height of right circular cylinder is 10 cm and radius of its base is 4 cm, find its total surface area?

A)

350 cm²


B)

351 cm²


C)

352 cm²


D)

353 cm²



Correct Answer :

352 cm²


Explanation :

Total Surface Area of a cylinder= 2πrh + 2πr2 = 2πr(h + r)
= 2* 22/7 * 4 *(10 + 4)
= 2* 22/7 * 4 * 14
= 2* 22 * 4 * 2
= 352 cm2

Length,Width and Height of a cuboid are in the ratio of 6:3:5. If the total surface area of cuboid is 1134 cm2 then find its Length, Width and Height.

A)
18, 9, 15

B)
17, 10, 15

C)
12, 15, 9

D)
11, 13, 16


Correct Answer :

18, 9, 15


Explanation :

Let the length,width and height of the cuboid are 6x,3x,5x respectively.

The total surface area of cuboid ,2*(lb + bh + lh) = 1134
=>2*(6x×3x+3x×5x+6x×5x) = 1134
=>18x2 + 15x2 + 30x2 = 567
=>63x2 = 567
=>x2 = 9
So x=3

Hence the dimensions of cuboid will be 18, 9, 15.

If the surface area of two spheres are in the ratio 9:16, then the ratio of their volumes will be?

A)

9:16


B)

16:9


C)

27:64


D)

3:4



Correct Answer :

27:64


Explanation :

Let the radius of two sphere be r and R

As is given, 4πr2/4πR2 = 9/16
r2/R2 = 9/16
r/R = 3/4

ratio of their volume = (4πr3/3) / (4πR3/3)
=r3/R3
=(r/R)3
=(3/4)3
=27/64

The volume of a cube is 512 cm3, Its surface area is ?

64 cm2
256 cm2
384 cm2
512 cm2

Correct Answer :

384 cm2


Explanation :

Volume =a3 = 512 cm3= 8 x 8 x 8
⇒ a = 8 cm
Then, Surface area = 6a2
=6 x (8)2 cm2
=384 cm2

A box is of 10 cm long, 8 cm broad and 5 cm high. What is the longest possible length of a pencil that can be put in ?

√150 cm
√98 cm
3√21 cm
3√52 cm

Correct Answer :

3√21 cm


Explanation :

Since, the box is in the form of a cuboid.

longest possible length of a pencil=>diagonal of cuboid=√(l2 +b2 +h2)
= √102 +82 + 52 cm
= √189
= √9 x 21
= 3√21 cm

Find the height of the cylinder whose volume is 551 m3 and the area of the base is 36.5 m2 ?

7 m
10.5 m
14 m
15 m

Correct Answer :

14 m


Explanation :

Base of cylinder => Area of circle = πr2 = 36.5 m2

Volume of cylinder = πr2h = Area base * height = 36.5 * h
551 = 36.5 x h
Hence height of the cylinder, h = 511/36.5 = 14 m

If the volume and surface are of a sphere are numerically the same then its radius is ?

1 unit
2 unit
3 unit
4 unit

Correct Answer :

3 unit


Explanation :

Volume = (4/3)πr3
Surface Area = 4πr2

as per question, 4/3 πr3 = 4πr2
⇒ r = 3 units.

A cylinder and a cone have the same height and same radius of the base. The ratio between the volumes of the cylinder and the cone is ?

A)
1 : 3

B)
3 : 1

C)
1 : 2

D)
2 : 1


Correct Answer :

3 : 1


Explanation :

Volume of Cylinder = πr2h

Volume of cone = (1/3)πr2h

Ratio of their volumes = [πr2h] / [(1/3)πr2h] => 3/1 => 3 : 1

A sphere of radius r has the same volume as that of a cone with circular base of radius r. Find the height of the cone ?

2r
r/3
4r
(2/3)r

Correct Answer :

4r


Explanation :

Volume of sphere = Volume of cone
⇒ (4/3)πr3 = (1/3)πr2h
⇒ 4r = h

If the volume of the cube is 1331 m3, then the total surface area of the cube is(in m2):

A)
648

B)
484

C)
726

D)
216


Correct Answer :

726


Explanation :

Let the side of Cube is a

Then,
Volume of Cube = a3 =1331 m3
a=11
So Surface Area of the cube is = 6a2 = 6* 112 =6*121
=726

The areas of two circles are in the ratio 1:2. Find the ratio of their radius?

A)
1:2

B)
1:3

C)
1:√2

D)
1:4


Correct Answer :

1:√2


Explanation :

Ratio of the areas of the circles = π(r1)2 : π(r2)2 =1:2
hence, (r1)2 : (r2)2 =1:2
(r1) : (r2) =1:√2

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