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

1 answer

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.