find the volume of the composite solid, which is a hemisphere atop a cylinder. note that the figure is not…

Explanation:

Step1: Calculate cylinder volume

The formula for the volume of a cylinder is $V_{cylinder}=\pi r^{2}h$. Here, $r = 4$ and $h=12$. So $V_{cylinder}=\pi\times4^{2}\times12=\pi\times16\times12 = 192\pi$.

Step2: Calculate hemisphere volume

The formula for the volume of a hemisphere is $V_{hemisphere}=\frac{2}{3}\pi r^{3}$. With $r = 4$, we have $V_{hemisphere}=\frac{2}{3}\pi\times4^{3}=\frac{2}{3}\pi\times64=\frac{128\pi}{3}$.

Step3: Calculate composite - solid volume

The volume of the composite solid $V = V_{cylinder}+V_{hemisphere}$. So $V=192\pi+\frac{128\pi}{3}=\frac{576\pi + 128\pi}{3}=\frac{704\pi}{3}$. Using $\pi\approx3.14159$, we get $V=\frac{704\times3.14159}{3}\approx737.27$.

Answer:

$737.27$