UPSC Prelims 1999 · General Studies
Question 149: Basic Numeracy
The area of an ellipse is twice that of a circle. The major diameter of the ellipse is twice that of the minor diameter. The radius of the circle is
AnswerThe answer is (a).
Let the minor diameter be d, so the minor semi-axis is d/2; the major diameter is 2d, so the major semi-axis is d. Ellipse area = pi x d x (d/2) = pi d squared / 2. This is twice the circle's area, so the circle's area is pi d squared / 4, meaning r squared = d squared / 4 and r = d/2. The radius is half the minor diameter, i.e. 50 per cent of it.
Why each option is right or wrong
- (a) Right. r = d/2, which is 50 per cent of the minor diameter.
- (b) Wrong. 50 per cent of the major diameter is d, which is twice the radius found.
- (c) Wrong. The minor diameter is d, which is twice the radius.
- (d) Wrong. The major diameter is 2d, four times the radius.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 1999, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.