Question

a bowl is in the shape of a hemisphere (half a sphere) with a diameter of 7 inches. find the volume of the bowl. use 3.14 for π. the volume of the bowl is about
(simplify your answer. round to two decimal places as needed.)

Explanation:

Step1: Find the radius

The diameter \( d = 7 \) inches, so the radius \( r=\frac{d}{2}=\frac{7}{2} = 3.5 \) inches.

Step2: Recall the volume formula for a hemisphere

The volume of a sphere is \( V_{sphere}=\frac{4}{3}\pi r^{3} \), so the volume of a hemisphere \( V_{hemisphere}=\frac{1}{2}\times\frac{4}{3}\pi r^{3}=\frac{2}{3}\pi r^{3} \).

Step3: Substitute the values

Substitute \( r = 3.5 \) and \( \pi=3.14 \) into the formula:
\( V=\frac{2}{3}\times3.14\times(3.5)^{3} \)
First, calculate \( (3.5)^{3}=3.5\times3.5\times3.5 = 42.875 \)
Then, \( \frac{2}{3}\times3.14\times42.875=\frac{2\times3.14\times42.875}{3}=\frac{270.045}{3}=90.015 \)

Step4: Round to two decimal places

\( 90.015\approx90.02 \)

Answer:

\( 90.02 \) cubic inches