Question

question
what is the volume of a hemisphere with a diameter of 51 m, rounded to the nearest tenth of a cubic meter?
answer attempt 1 out of 2
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Explanation:

Step1: Find the radius

The radius \( r \) of a sphere (and hemisphere) is half of the diameter. Given \( d = 51\) m, so \( r=\frac{d}{2}=\frac{51}{2}=25.5\) m.

Step2: Use the formula for the volume of a hemisphere

The volume formula for a hemisphere is \( V=\frac{2}{3}\pi r^{3}\).
Substitute \( r = 25.5\) into the formula:
\( V=\frac{2}{3}\pi(25.5)^{3}\).
First, calculate \( (25.5)^{3}=25.5\times25.5\times25.5 = 16581.375\).
Then, \( V=\frac{2}{3}\times\pi\times16581.375\).
\( V=\frac{33162.75}{3}\pi\).
\( V = 11054.25\pi\).
Using \( \pi\approx3.14159\), we get \( V\approx11054.25\times3.14159\).
\( V\approx34735.2\) (rounded to the nearest tenth).

Answer:

\( 34735.2\)