Question

The radius of a sphere is increased by 10% . prove that the volume will be increased by 33.1 % .

Answer 1

let the initial radius be R
new radius = R + R* 10/100 = 11R/10
initial volume = 4/3 * pie * R^3
new volume = 4/3 * pie * (11R/10)^3
% increase in volume = new volume/ initial volume * 100
                                    = 11/10 * 11/10 *11/10 *100 = 1331/10 = 133.1 %
so, the volume is increased by 133.1 % and not by 33.1 %. ANSWER.
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