UPSC Prelims 1999 · General Studies
Question 144: Basic Numeracy
A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is the same for both bowl and cylinder, then the volume of the beverage in the cylindrical vessel will be
AnswerThe answer is (c).
The bowl and the cylinder have the same diameter, so the same radius r. A hemisphere has volume (2/3) x pi x r cubed. The cylinder's radius is 50 per cent more than its height, so r = 1.5h and h = 2r/3; its volume is pi x r squared x h = pi x r squared x 2r/3 = (2/3) x pi x r cubed. The volumes are equal, so the beverage exactly fills the cylinder: 100 per cent.
Why each option is right or wrong
- (a) Wrong. The volumes are equal, so it is not two thirds.
- (b) Wrong. It does not fill only 78.75 per cent.
- (c) Right. The cylinder holds exactly the bowl's contents.
- (d) Wrong. Nothing is left over in the bowl.
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.