Question

A ballon is being filled by air so that it's volume V is gradually increasing.Find the rate of increase of volume with radius r when r = 2 units.​

Answer 1

Q. A ballon is being filled by air so that it's volume V is gradually increasing.Find the rate of increase of volume with radius r when r = 2 units.

Ans:- 16 π

Explanation:-

$the \: volume \: of \: spherical \: ballon \: is \:$

$v = \frac{4}{3} \pi {r}^{3}$

The rate of increase of V with respect to the radius r is :-

$\frac{dv}{dr} = \frac{d}{dr} ( \frac{4}{3} \pi {r}^{3} )$

$\frac{dv}{dr} = \frac{4}{3} \pi. \frac{d}{dr} ( {r}^{3} )$

$\frac{4}{3} \pi.3 {r}^{2}$

$4\pi {r}^{2}$

$when \: r = 2$

$\frac{dv}{dr} = 4\pi {2}^{2}$

$16\pi$