Question

the volume of sphere increases at the rateof 2cm³/sec find the rate of change of its surface area when it's radius is 5cm​

Answer 1

Answer:

We know that,

Volume of sphere=34πr3            (If radius r)

i.e.V=34πr3

Differentiating equation with respect to t  and we get,

dtdV=34π.3r2dtdr

⇒dtdV=4πr2dtdr.......(1)

Given that, dtdV=3c.m.3/sec.    and r=2c.m.

By equation (1) to and we get,

3=4π(2)2dtdr

dtdr=16π3c.m./sec.

Now, let S be the surface area

Then,

S=4πr2

When

dtdS=8πrdt