find the derivative of volume with respect to height.
find the derivative of volume with respect to height.
Answer
Explanation:
Step1: Recall volume formula
The volume formula for a cylinder is $V=\pi r^{2}h$, where $r$ is the radius and $h$ is the height. Here, assume $r$ is a constant.
Step2: Apply derivative rule
The derivative of $V$ with respect to $h$, using the power - rule $\frac{d}{dh}(ah)=a$ (where $a = \pi r^{2}$ is a constant), we have $\frac{dV}{dh}=\pi r^{2}$.
Answer:
$\pi r^{2}$