Question

Use the formula for the volume of a sphere to solve the following problem.
How much air is needed to fill a basketball with a diameter of 9 inches? Use 3.14 as an approximation for pi. Round your answer to the nearest tenth.

3,052.1
113
190.8
381.5

Answer 1

To find the volume of a basketball (a sphere), we can use the formula for the volume of a sphere:

\[
V = \frac{4}{3} \pi r^3
\]

where \(V\) is the volume and \(r\) is the radius of the sphere.

Given that the diameter of the basketball is 9 inches, we can find the radius by dividing the diameter by 2:

\[
r = \frac{9}{2} = 4.5 \text{ inches}
\]

Now we can substitute the radius into the volume formula. Using 3.14 as the approximation for \(\pi\):

\[
V = \frac{4}{3} \times 3.14 \times (4.5)^3
\]

First, we need to calculate \( (4.5)^3 \):

\[
(4.5)^3 = 4.5 \times 4.5 \times 4.5 = 20.25 \times 4.5 = 91.125
\]

Now we can substitute this value back into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times 91.125
\]

Calculating \( \frac{4}{3} \times 3.14 \):

\[
\frac{4}{3} \times 3.14 \approx 4.1867
\]

Now we multiply:

\[
V \approx 4.1867 \times 91.125 \approx 381.5
\]

Thus, the volume of air needed to fill the basketball is approximately:

\[
\boxed{381.5} \text{ cubic inches}
\]