Question

what is the volume of a hemisphere with a radius of 6.1 ft, rounded to the nearest tenth of a cubic foot?

Explanation:

Step1: Recall the formula for the volume of 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 the radius \( r = 6.1\) ft. Substituting this value into the formula, we get:
\( V=\frac{2}{3}\pi(6.1)^{3} \)

First, calculate \( (6.1)^{3} \). \( 6.1\times6.1 = 37.21 \), and then \( 37.21\times6.1=226.981 \).

So now the formula becomes \( V=\frac{2}{3}\pi\times226.981 \)

Step3: Calculate the value of the volume.

First, calculate \( \frac{2}{3}\times226.981=\frac{453.962}{3} = 151.320\overline{6} \)

Then multiply by \( \pi \) (using \( \pi\approx3.14159 \)): \( V\approx151.320\overline{6}\times3.14159 \)

\( 151.320\overline{6}\times3.14159\approx475.2 \) (rounded to the nearest tenth)

Answer:

The volume of the hemisphere is approximately \( 475.2 \) cubic feet.