The volume of metal in a hollow sphere is constant. If the inner radius is increasing at the rate of 1 cm/sec, find the rate of increase of the outer radius when the radii are 4 cm and 8 cm respectively.

Explanation

Volume of a hollow sphere is given by,

`V = 4/3pi(R^3 - r^3)`, where `R` is outer radius and `r` is inner radius.

Here, it is given that `r = 4cm and R = 8cm.`

Now,

`(dV)/dt = 4/3pi[3R^2(dR)/dt - 3r^2(dr)/dt]->(1)`

It is given that volume remains constant.

`:. (dV)/dt = 0`

Also, `(dr)/dt = 1` cm/sec

...