Surface area Suppose that the radius rr and surface area S=4πr2S=4πr^{2} of a sphere are differentiable functions of tt. Write an equation that relates dS/dtdS/dt to dr/dtdr/dt.

Surface area Suppose that the radius rr and surface area $S=4\pi r2S=4\pi {r}^{2}$
of a sphere are differentiable functions of tt. Write an equation that relates dS/dtdS/dt to dr/dtdr/dt.
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

hajavaF

$\frac{dS}{dt}=8pir\frac{dr}{dt}$ Knowing implicit differentiation and the given equation, we can take the derivative with respect to t. Doing this we get $\frac{dS}{dt}=8\pi r\frac{dr}{dt}$. We get this by using implicit differentiation and going left to right throughout the problem.

Not exactly what you’re looking for?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee