Question

the radius of a sphere is 10 cm. if the radius is increased by 1cm. then prove that the volume of the sphere is increased by 33.1%

Answer 1

Let the initial radius of sphere be r. Then, the volume of the sphere is given by 43πr343πr3

Now, let new radius be r'. Then, r′=r+10100∗rr′=r+10100∗r

r′=1110∗rr′=1110∗r

Now, the new volume of the sphere = 43πr′343πr′3

=>New volume  = 43π11103r343π11103r3

% increase in volume = Newvolume−OldVolumeOldVolume∗100Newvolume−OldVolumeOldVolume∗100

% increase in volume = 43π(1110)3r3−43πr343πr3∗10043π(1110)3r3−43πr343πr3∗100

Remove 43πr343πr3from both the numerator and denominator.

% increase in volume = ((1110)3−1)∗100((1110)3−1)∗100

% increase in volume = 113−10310113−10310

% increase in volume = 1331−1000101331−100010

% increase in volume = 3311033110

% increase in volume = 33.1
Hence proved
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