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

Explanation:

Step1: Calculate cone volume

The formula for the volume of a cone is $V_{cone}=\frac{1}{3}\pi r^2 h$. Here, $r=5$, $h=14$. $V_{cone}=\frac{1}{3}\pi (5)^2 (14)=\frac{1}{3}\pi \times25\times14=\frac{350}{3}\pi$

Step2: Calculate hemisphere volume

The formula for the volume of a hemisphere is $V_{hemisphere}=\frac{2}{3}\pi r^3$. Here, $r=5$. $V_{hemisphere}=\frac{2}{3}\pi (5)^3=\frac{2}{3}\pi \times125=\frac{250}{3}\pi$

Step3: Sum the two volumes

Add the volume of the cone and hemisphere to get the total volume. $V_{total}=\frac{350}{3}\pi+\frac{250}{3}\pi=\frac{600}{3}\pi=200\pi$

Step4: Compute numerical value

Use $\pi\approx3.1416$ to find the decimal value. $V_{total}\approx200\times3.1416=628.32$

Answer:

$628.32$