Problem 36E

36. A faucet is filling a hemispherical basin of diameter $60 \mathrm{~cm}$ with water at a rate of $2 \mathrm{~L} / \mathrm{min}$. Find the rate at which the water is rising in the basin when it is half full. [Use the following facts: $1 \mathrm{~L}$ is $1000 \mathrm{~cm}^{3} .$ The volume of the portion of a sphere with radius $r$ from the bottom to a height $h$ is $V=\pi\left(r h^{2}-\frac{1}{3} h^{3}\right)$, as we will show in Chapter $\left.5 .\right]$


Step-by-Step Solution