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

in.
3
190.8 inches cubed

3,052.1 in.3
3
,
052.1

in.
3
3,052.1 inches cubed

381.5 in.3
381.5

in.
3
381.5 inches cubed

113 in.3 :P

1 answer

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

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

Where \( r \) is the radius of the sphere. The radius is half of the diameter. Thus:

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

Now, substituting \( r \) into the volume formula:

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

Calculating \( (4.5)^3 \):

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

Now substitute \( \pi \) with 3.14:

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

Calculating the volume step-by-step:

  1. Calculate \( \frac{4}{3} \times 3.14 \): \[ \frac{4}{3} \times 3.14 \approx 4.1867 \]

  2. Now multiply by \( 91.125 \): \[ V \approx 4.1867 \times 91.125 \approx 381.5 , \text{in}^3 \]

Therefore, the volume of the basketball is approximately 381.5 inches cubed.

The correct answer is:

381.5 in.³