Review question

# If we increase $r$ by a small amount, what happens to $A$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5329

## Question

A closed circular cylinder has height $16$ in. and radius $r$ in. The total surface area is $A$ sq. in.

Prove that $\begin{equation*} \frac{dA}{dr} = 4\pi(r+8). \end{equation*}$

Use this result to calculate an approximation for the increase in area when the radius increases from $4$ to $4.02$ in., the height remaining constant. You may leave the answer in terms of $\pi$.