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what is the volume of a hemisphere with a diameter of 6.1 cm, rounded to the nearest tenth of a cubic centimeter?
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Explanation:

Step1: Find the radius

The diameter \( d = 6.1 \) cm, so the radius \( r=\frac{d}{2}=\frac{6.1}{2} = 3.05 \) cm.

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 \( r = 3.05 \) into the formula: \( V=\frac{2}{3}\pi(3.05)^{3} \).
First, calculate \( (3.05)^{3}=3.05\times3.05\times3.05 = 3.05\times9.3025=28.372625 \).
Then, \( \frac{2}{3}\times\pi\times28.372625=\frac{56.74525}{3}\pi\approx\frac{56.74525}{3}\times3.14159265 \).
\( \frac{56.74525}{3}\approx18.915083 \), and \( 18.915083\times3.14159265\approx59.4 \) (rounded to the nearest tenth).

Answer:

\( 59.4 \)