1. ## Related rates

The volume V of a sphere changes with time according to the equation:
$\displaystyle V=35\pi + \pi t^2$

Find the rate of change of the surface area of sphere when t=1sec ?

Am solving problems for fun
and i really stopped at this one

ok $\displaystyle S=4 \pi r^2$

and $\displaystyle V=\frac{4}{3} \pi r^3$

the problem here is that there is no value for r in the problem

2. Originally Posted by TWiX
The volume V of a sphere changes with time according to the equation:
$\displaystyle V=35\pi + \pi t^2$

Find the rate of change of the surface area of sphere when t=1sec ?

Am solving problems for fun
and i really stopped at this one

ok $\displaystyle S=4 \pi r^2$

and $\displaystyle V=\frac{4}{3} \pi r^3$

the problem here is that there is no value for r in the problem
Can't you find r in terms of t by saying that $\displaystyle \frac{4}{3} \pi r^3 = 35\pi + \pi t^2$ which simplifies to $\displaystyle r = \sqrt[3]{\frac{105+3t^2}{4}}$
$\displaystyle \frac{dS}{dt} = \frac{dS}{dr} \cdot \frac{dr}{dt}$