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

3,052.1 in.3
3,052.1 inches cubed

113 in.3
113 inches cubed

190.8 in.3

Answer 1

To calculate the volume of a sphere, we use the formula:

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

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

Given:
- The diameter of the basketball is 9 inches, so the radius \( r \) is half of the diameter:

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

Now we can substitute \( r \) and \(\pi \) into the volume formula. Using \( \pi \approx 3.14 \):

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

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 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 \( 4.1867 \) by \( 91.125 \):

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

Rounding to the nearest tenth, the volume of air needed to fill the basketball is:

\[
\approx 381.5 \text{ in}^3
\]

Thus, the answer is:

**381.5 in.³ or 381.5 inches cubed.**