Question

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. 113 in.3
2. 3,052.1 in.3
3. 190.8 in.3
4. 381.5 in.3

Answer 1

To find the volume of a basketball (which is a sphere) with a diameter of 9 inches, we can use the formula for the volume of a sphere:

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

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

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

Now we can plug the radius 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 back into the volume formula:

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

Calculating the multiplication:

\[
3.14 \times 91.125 \approx 285.1975
\]

Now multiply by \( \frac{4}{3} \):

\[
V = \frac{4 \times 285.1975}{3} \approx \frac{1140.79}{3} \approx 380.2633
\]

Rounding to the nearest tenth:

\[
V \approx 380.3 \text{ in}^3
\]

Now, looking at the options provided:

1. 113 in³
2. 3,052.1 in³
3. 190.8 in³
4. 381.5 in³

The closest answer is **4. 381.5 in³**.