Question

what is the volume of a hemisphere with a diameter of 7.1 ft, rounded to the nearest tenth of a cubic foot?

Explanation:

Step1: Find the radius

The diameter \( d = 7.1\) ft, so the radius \( r=\frac{d}{2}=\frac{7.1}{2} = 3.55\) ft.

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 \( r = 3.55\) into the formula: \( V=\frac{2}{3}\pi(3.55)^{3}\). First, calculate \( (3.55)^{3}=3.55\times3.55\times3.55 = 44.909375\). Then, \( \frac{2}{3}\times\pi\times44.909375\approx\frac{2}{3}\times3.1416\times44.909375\). Calculate \( \frac{2}{3}\times3.1416\approx2.0944\). Then, \( 2.0944\times44.909375\approx94.1\) (rounded to the nearest tenth).

Answer:

The volume of the hemisphere is approximately \( 94.1\) cubic feet.