Question

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

Answer 1

Answer:

33.1%

Step-by-step explanation:

Let the initial radius of the sphere be r.

 initially, volume of sphere = 4/3 πr³

                                          = V(say)

When the radius is increased by 10%,

New radius is r + 10% of r

                    = r + 0.1r = 1.1r

new volume = 4/3 π (1.1r)³

                     = 1.331 (4/3 πr³)

                     = 1.331 (V)

Increase% = increase/initial  *100%

     = (1.331 V - V)/V  * 100%

     = (0.331) * 100%

     = 33.1%

Proved

Answer 2

Answer :-

Let the volume = v

Radius == r

Now

When r increased by 10%

r + 10% of r

r + 0.1r = 0.1 + 1 = 1.1r

Now

Volume =  4/3 π (1.1r)³

V = 4/3 * 22/7 (1.331r)

1.331 (v)

Now

Increase % = (1.331v - v)/v * 100%

Increase = 0.331v/v *100

Increase = 0.331 * 100 = 33.1%