Question

question
what is the volume of a hemisphere with a radius of 6.5 in, rounded to the nearest tenth of a cubic inch?
answer attempt 2 out of 2
in^3
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Explanation:

Step1: Recall the volume formula for a hemisphere

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

Step2: Substitute the given radius into the formula

We are given that \( r = 6.5 \) inches. Substitute \( r=6.5 \) into the formula:
\[

$$\begin{align*} V&=\frac{2}{3}\pi(6.5)^{3}\\ &=\frac{2}{3}\pi\times274.625\\ &=\frac{549.25}{3}\pi\\ &\approx\frac{549.25}{3}\times3.14159 \end{align*}$$

\]

Step3: Calculate the numerical value

First, calculate \( \frac{549.25}{3}\approx183.0833 \). Then multiply by \( \pi\approx3.14159 \):
\[
183.0833\times3.14159\approx575.958
\]
Rounding to the nearest tenth, we get \( 576.0 \) (since the hundredth digit is 5, we round up the tenth digit).

Answer:

\( 576.0 \)