Question

what is the volume of a hemisphere with a diameter of 30.3 ft, rounded to the nearest tenth of a cubic foot?

Explanation:

Step1: Find the radius

The diameter \(d = 30.3\) ft, so the radius \(r=\frac{d}{2}=\frac{30.3}{2} = 15.15\) ft.

Step2: Recall the volume formula for a hemisphere

The volume \(V\) of a hemisphere is given by \(V=\frac{2}{3}\pi r^{3}\).

Step3: Substitute the radius into the formula

Substitute \(r = 15.15\) into the formula:
\[

$$\begin{align*} V&=\frac{2}{3}\pi(15.15)^{3}\\ &=\frac{2}{3}\pi\times15.15\times15.15\times15.15\\ &=\frac{2}{3}\pi\times3474.871875\\ &\approx\frac{2}{3}\times3.14159\times3474.871875\\ &\approx2.09439\times3474.871875\\ &\approx7272.5 \end{align*}$$

\]

Answer:

\(7272.5\) cubic feet