UPSC Prelims 1997 · General Studies

Question 140: Basic Numeracy

If the number representing volume and surface area of a cube are equal, then the length of the edge of the cube in terms of the unit of measurement will be

AnswerThe answer is (d).

For a cube of edge a, volume = a³ and surface area = 6a². Setting a³ = 6a² and dividing by a² gives a = 6, in the same unit of measurement. The numbers match only for this one edge length, because volume grows with the cube of the edge and surface area with its square. Remember the answer as 6.

Why each option is right or wrong

(a) For a = 3, volume is 27 and surface area is 54.
(b) For a = 4, volume is 64 and surface area is 96.
(c) For a = 5, volume is 125 and surface area is 150.
(d) Right: for a = 6, volume and surface area are both 216.

Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 1997, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.