Question

22. The radius of a sphere is 10 cm. If the radius is increased by 1 cm. Then prove that
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 43πr3

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

r′=1110∗r

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

=>New volume  = 43π11103r3

% increase in volume = Newvolume−OldVolumeOldVolume∗100

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

Remove 43πr3from both the numerator and denominator.

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

% increase in volume = 113−10310

% increase in volume = 1331−100010

% increase in volume = 33110

% increase in volume = 33.1

hence proved

Answer 2

Answer: Here's the proof:

Step-by-step explanation: volume of sphere = 4/3πr³

hence, r=10

4/3π10³

=4186.67 cm³

increasing the radius by 1 cm gives 11 cm

hence, 4/3πr³

4/3π11³

=5572.45 cm³

take the difference

5572.45-4186.67

=1385.78

as a percentage of the initial volume,

(1385.78÷4186.67)×100%

=33.09%

=33.1%