Problem 10 - Entrance Test

If the surface area of a sphere is 616 cm², its volume is

A. 1437⅓ cm³B. 1437⅔ cm³C. 1438⅓ cm³D. 1438⅔ cm³

Correct: A

Surface area=4πr²=616 → r²=616·1/(4π)=154/π → r=√(154/π). Volume=4/3 πr³=4/3 π·(154/π)·√(154/π)=4/3·154·√(154/π). With π=22/7, 154/π=154·7/22=49, so r=7. Then volume=4/3π(7³)=4/3·22/7·343=4/3·22·49=4312/3=1437⅓.