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.

(1 point)
Responses

381.5 in.3
381.5 inches cubed

113 in.3
113 inches cubed

190.8 in.3
190.8 inches cubed

3,052.1 in.3

Answer 1

To find the volume of a basketball (which is 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, \( \pi \) is approximately 3.14, and \( r \) is the radius of the sphere.

First, we need to find the radius of the basketball. The diameter is given as 9 inches, so the radius \( r \) is half of the diameter:

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

Now we can substitute the radius into the volume formula:

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

Calculating \( (4.5)^3 \):

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

Now, substituting 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, multiply this by \( 91.125 \):

\[
V \approx 4.1867 \times 91.125 \approx 381.5 \text{ cubic inches}
\]

Rounding to the nearest tenth, we find:

\[
V \approx 381.5
\]

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

**381.5 in.³** (or 381.5 inches cubed).