UPSC Prelims 1998 · General Studies
Question 138: Basic Numeracy
A square pond has 2 m sides and is 1 m deep. If it is to be enlarged, the depth remaining the same, into a circular pond with the diagonal of the square as diameter as shown in the figure, then what would be the volume of earth to be removed?
AnswerThe answer is (a).
The square pond has volume 2 x 2 x 1 = 4 cubic metres. Its diagonal is 2 root 2 m, which is the diameter of the circular pond, so the radius is root 2 m and the area is pi x 2 = 2 pi square metres. At the same depth of 1 m the volume is 2 pi cubic metres. The earth to be removed is 2 pi - 4 cubic metres.
Why each option is right or wrong
- (a) Right: 2 pi - 4 cubic metres.
- (b) 4 pi - 4 would result from a radius of 2 m, not root 2 m.
- (c) 4 pi - 2 uses a wrong radius and a wrong old volume.
- (d) 2 pi - 2 uses the wrong volume of the square pond.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 1998, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.