# Math Help - Related Rates (implicit differentiation)

1. ## Related Rates (implicit differentiation)

Air is being pumped into a spherical balloon so that its volume increases at a rate of 80cm^3/s . How fast is the surface area of the balloon increasing when its radius is 11cm ?

... i found the derivative of Surface Area to be 8*pi*r*(dv/dt)=(ds/dt)

i keep getting 7040*pi as my answer.. but its not correct.

please help mee!

2. The volume of a sphere is given by $V=\frac{4}{3}{\pi}r^{3}$

$\frac{dV}{dt}=4{\pi}r^{2}\cdot \frac{dr}{dt}$

You have all the info to sub into the above derivative and solve for dr/dt.

Then, you can use that result in the surface area derivative.

$\frac{dS}{dt}=8{\pi}r\cdot \frac{dr}{dt}$ and solve.