Question

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

190.8 in.3
190.8 inches cubed

3,052.1 in.3
3,052.1 inches cubed

113 in.3
113 inches cubed

381.5 in.3

Answer 1

To find the volume of a sphere, you can use the formula:

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

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

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

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

Now we can substitute the radius and the approximation for \( \pi \) 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 back into the volume formula:

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

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

\[
\frac{4}{3} \times 3.14 \approx 4.18667
\]

Now multiplying by \( 91.125 \):

\[
V \approx 4.18667 \times 91.125 \approx 381.5
\]

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

\[
\boxed{381.5 \text{ in.}^3}
\]