Question

9. The radius of sphere is increasing at a rate of 3cm/minute. Find the rate of change of volume

when r=2cm *

V = 12
48л
16л
64 л
32T

Answer 1

48π

Explanation:

Given that,

The radius of the sphere is increasing at a rate of 3cm/minute,
`(dr)/(dt)=3\ cm/minute`

The volume of a sphere is given by :

`V=(4)/(3)\pi r^3`

Differentiating both sides wrt t.

`(dV)/(dt)=(4)/(3)\pi * 3r^2* (dr)/(dt)\\\\=4\pi r^2* (dr)/(dt)`

Put r = 2 cm and dr/dt = 3 cm/minute

So,

`(dV)/(dt)=4\pi r^2* (dr)/(dt)\\\\(dV)/(dt)=4\pi * 2^2* 3\\\\(dV)/(dt)=48\pi`

Hence, the correct option is (a) "48π".