UPSC Prelims 2002 · General Studies

Question 20: Basic Numeracy

Consider the volumes of the following:

1.A parallelepiped of length 5 cm, breadth 3 cm and height 4 cm
2.A cube of each side 4 cm
3.A cylinder of radius 3 cm and length 3 cm
4.A sphere of radius 3 cm The volumes of these in the decreasing order is

aI, III, II, IV

bIV, II, III, I

cI, II, III, IV

dIV, III, II, I

AnswerThe answer is (d).

Work out each volume. I: 5 x 3 x 4 = 60 cm3. II: 4 x 4 x 4 = 64 cm3. III: pi r-squared h = pi x 9 x 3 = 27 pi, about 84.8 cm3. IV: 4/3 pi r-cubed = 4/3 x pi x 27 = 36 pi, about 113.1 cm3. Decreasing order is IV (113.1), III (84.8), II (64), I (60).

1. Parallelepiped: 5 x 3 x 4 = 60 cm3, the smallest (fourth).
2. Cube: 4 x 4 x 4 = 64 cm3, third.
3. Cylinder: pi x 9 x 3 = 27 pi, about 84.8 cm3, second.
4. Sphere: 4/3 x pi x 27 = 36 pi, about 113.1 cm3, the largest.

Why each option is right or wrong

(a) I is the smallest volume, so it cannot come first.
(b) Puts the cube above the cylinder, but 64 is less than 84.8.
(c) This is ascending order, the reverse of what is asked.
(d) Right: 113.1 > 84.8 > 64 > 60.

Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2002, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.