find the volume of each hemisphere. round to the nearest tenth. (example 4) 8. 6.8 ft 9. 1.8 mm

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Accepted Answer

# Explanation:
## Step1: Recall the formula for the volume of a hemisphere
The volume $V$ of a hemisphere is given by $V=\frac{2}{3}\pi r^{3}$, where $r$ is the radius of the hemisphere.
## Step2: Solve for problem 8
Given $r = 6.8$ ft.
Substitute $r = 6.8$ into the formula:
$$
\begin{align*}
V&=\frac{2}{3}\pi(6.8)^{3}\
&=\frac{2}{3}\pi(314.432)\
&=\frac{628.864}{3}\pi\
&\approx\frac{628.864}{3}\times3.14\
&=\frac{1974.63296}{3}\
&\approx658.2
\end{align*}
$$
## Step3: Solve for problem 9
Given $r = 1.8$ mm.
Substitute $r = 1.8$ into the formula:
$$
\begin{align*}
V&=\frac{2}{3}\pi(1.8)^{3}\
&=\frac{2}{3}\pi(5.832)\
&=\frac{11.664}{3}\pi\
&\approx\frac{11.664}{3}\times3.14\
& = 3.888\times3.14\
&\approx12.2
\end{align*}
$$

# Answer:
8. $658.2$ ft³
9. $12.2$ mm³

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the volume of a hemisphere

Step2: Solve for problem 8

Step3: Solve for problem 9

Answer: