Volume and Surface Area- Aptitude Questions and Answers

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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 ?

A) √150 cm
B) √98 cm
C) 3√21 cm
D) 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

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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 ?

A) 64 cm2
B) 256 cm2
C) 384 cm2
D) 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

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

A) 7 m
B) 10.5 m
C) 14 m
D) 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 ?

A) 1 unit
B) 2 unit
C) 3 unit
D) 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 ?

A) 2r
B) r/3
C) 4r
D) (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

A hall is 12m long and 8m broad. If the sum of the area of the floor and the ceiling is equal to the sum of the area of the four walls. Find the height of the hall (in m)

A)
4.8

B)
6.4

C)
8.3

D)
3.2


Correct Answer :

4.8


Explanation :

Area of 4 walls of a room = (l*h)+(b*h)+(l*h)+(b*h) =2(l*h)+2(b*h) = 2h(l+b)
Area of the floor + Area of ceiling =>(l*b) +(l*b) => 2*(l*b)

We have,
Area of 4 walls of a room= Area of the floor + Area of ceiling
Hence,
2 * h*(12 + 8) = 2*(12 * 8)
h = 96/20 = 4.8 m

If each side of a cube is 3 centimeter,then its surface area is :

A)

54 Cubic Centimeter


B)

9 Square Centimeter


C)

54 Square Centimeter


D)

None of these



Correct Answer :

54 Square Centimeter


Explanation :

if side of the square as “a”, then
Surface area of a cube = 6a2 = 6*(3)2 = 54 cm2

A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to the smaller cubes?

A)

1/6


B)

1/5


C)

1/25


D)

1/125



Correct Answer :

1/5


Explanation :

The volume of the original cube = 53 = 125 cm3.
The volume of a smaller cubes = 13 = 1 cm3.
Therefore, we will be get total smaller cubes = 125/1 = 125

The surface area of the larger cube = 6*a2 = 6(52) = 6 * 25 = 150
The surface area of each of the smaller cubes = 6 (12) = 6.
Therefore, surface area of all of the 125, 1 cm3 cubes = 125 * 6 = 750.

Hence, the required ratio = 150 / 750 = 1 / 5

If the surface area of sphere is 346.5 cm2, then its radius is [ taking π=22/7 ]?

A)

5.25 cm


B)

7.25 cm


C)

3.25 cm


D)

9.25 cm



Correct Answer :

5.25 cm


Explanation :

Surface area of sphere= 4πr2
4 * 22/7 * r2 = 346.5
r2 = 346.5 * 7 / 4 * 22 = 27.5625
r = √27.5625 = 5.25 cm

If cost of painting is Rs 12 per sq meter of surface area, how much will it cost to paint all surfaces of a solid right circular cylinder with height of 9 meters and base area of 154 sq meters?

A)

Rs. 8448


B)

Rs. 9372


C)

Rs. 1540


D)

Rs. 3180



Correct Answer :

Rs. 8448


Explanation :

Base area of cylinder = πr2 = 154
r2 = 49
Thus, radius, r = 7

Then, Total Surface Area of cylinder = 2πr(h + r) = 2π*7*(9 + 7)
= 2* 22/7 * 7 *(9 + 7)
= 704

Hence, Cost of painting = 12 * 704
= Rs 8448

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