Learn and practice the chapter "Volume and Surface Area" with these solved Aptitude Questions and Answers. Each question in the topic is accompanied by a clear and easy explanation, diagrams, formulae, shortcuts and tricks that help in understanding the concept.

Use of Volume and Surface Area Questions

The questions and examples given in this section will be useful to all the freshers, college students and engineering students preparing for placement tests or any competitive exam like MBA, CAT, MAT, SNAP, MHCET, XAT, NMAT, GATE, Bank exams - IBPS, SBI, RBI, RRB, SSB, SSC, UPSC etc.

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1. A magician has a box of dimensions 10cm X 12cm X 8 cm. What can be the maximum length of the magic wand that he can keep in this box?

a. 277 cm
b. 10 cm
c. 12 cm
d. 1411 cm

Answer: a. 277 cm

Explanation:

Here the maximum possible length will be the diagonal length.

Tip:
Diagonal of cuboid/room/tank/Box = L^{2}+B^{2}+H^{2}
L = Length ; B = Breadth; H = Height

Maximum possible length of magic wand = 12^{2}+10^{2}+8^{2} = 308 ∴ Maximum possible length of magic wand =308 = 2 x 2 x 77 = 277

2. I have a big box of volume 8160 cu.cm. How many small pizza boxes of dimension 4cm X 3cm X 2 cm can I store in this big box?

a. 310
b. 320
c. 340
d. 375

Answer: c. 340

Explanation:

Volume of one box = length x breadth x height = 4 x 3 x 2 = 24 cu.cm.

Maximum number of boxes =

Cube volume

=

8160

= 340 boxes

One box volume

24

3. The dimensions of a wooden plank are in the ration 6:5:3. Its surface area is 504 sq. m. Find the breadth of the plank.

a. 23 sq.m
b. 53 sq.m
c. 102 sq.m.
d. 22 sq.m.

Answer: c. 102 sq.m.

Explanation:

Let the common factor be K
∴ Length = 6K ; Breadth = 5K and Height = 3K

Tip:
Total Surface area of cuboid = 2(LB + BH + LH)
L = Length; B = Breadth/width; H = Height

Whole surface area of the rectangular plank = 2(6K x 5K + 5K x 3K + 6K + 3K)
∴ 504 = 63K^{2}
∴ K = 22 ∴ Breadth = 5K = 102sq.m

4. What is the fall in the surface area of a cube if each of its sides is reduced by 21%?

a. -33.33%
b. 21%
c. 37.59%
d. 38.47%

Answer: c. 37.59%

Explanation:

Tip:
If you change any 2 surface area dimensions of a cube, cuboid, sphere, cylinder or cone, by say a% and b% respectively, then

Change in its surface area =

a+b +

ab

%

100

a and b is '-' for decrease AND '+' for increase

Here for a cube all sides are same. So change in two dimensions will be same.
∴ a = b = 21% decrease = -21

Change in its surface area =

-21-21 +

(-21)(-21)

%

100

∴ Change in its surface area = (-42+4.41)% = -37.59% There would be decrease of 37.59%

5. The ratio of the dimensions of two cylindrical drums are as follows.
Radii - 4:7
Heights - 21:8
Find the ratio of their volumes.

a. 2:3
b. 3:2
c. 6:7
d. 7:6

Answer: c. 6:7

Explanation:

Tip:
Volume of solid cylinder = πr^{2}h
R = Radius and h = Height

Since π is constant, Ratio of volumes can be directly given by