question
what is the volume of a hemisphere with a diameter of 54.8 in, rounded to the nearest tenth of a cubic inch?
answer attempt 2 out of 2
in³
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# Explanation:
## Step1: Find the radius
The diameter $ d = 54.8 $ in, so radius $ r=\frac{d}{2}=\frac{54.8}{2} = 27.4 $ in.
## 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 = 27.4 $ into the formula:
$$
\begin{align*}
V&=\frac{2}{3}\times\pi\times(27.4)^{3}\
&=\frac{2}{3}\times\pi\times27.4\times27.4\times27.4\
&=\frac{2}{3}\times\pi\times20798.984\
&\approx\frac{2}{3}\times3.14159\times20798.984\
&\approx\frac{65330.7}{3}\
&\approx 21776.9
\end{align*}
$$

# Answer:
$ 21776.9 $

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QUESTION IMAGE

Question

Explanation:

Step1: Find the radius

Step2: Recall the volume formula for a hemisphere

Step3: Substitute the radius into the formula

Answer: