Question

question
what is the volume of a hemisphere with a diameter of 7.7 ft, rounded to the nearest tenth of a cubic foot?
answer attempt 1 out of 2
ft³
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Explanation:

Step1: Find the radius

The diameter \( d = 7.7 \) ft, so the radius \( r=\frac{d}{2}=\frac{7.7}{2} = 3.85 \) ft.

Step2: Recall the volume formula for a hemisphere

The volume of a sphere is \( V_{sphere}=\frac{4}{3}\pi r^{3} \), so the volume of a hemisphere is \( V_{hemisphere}=\frac{1}{2}\times\frac{4}{3}\pi r^{3}=\frac{2}{3}\pi r^{3} \).

Step3: Substitute the radius into the formula

Substitute \( r = 3.85 \) into \( V_{hemisphere}=\frac{2}{3}\pi r^{3} \):
\[

$$\begin{align*} V&=\frac{2}{3}\times\pi\times(3.85)^{3}\\ &=\frac{2}{3}\times\pi\times3.85\times3.85\times3.85\\ &=\frac{2}{3}\times\pi\times57.066875\\ &\approx\frac{2}{3}\times3.14159\times57.066875\\ &\approx\frac{2\times3.14159\times57.066875}{3}\\ &\approx\frac{358.337}{3}\\ &\approx119.4 \end{align*}$$

\]

Answer:

\( 119.4 \)