Use the formula for the volume of a sphere to solve the following problem.

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 point)
Responses

113 in.3

190.8 in.3

381.5 in.3

3,052.1 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.

1. First, calculate the radius of the basketball. The diameter is 9 inches, so the radius \( r \) is:

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

2. Now, substitute \( r \) and \( \pi \approx 3.14 \) into the volume formula:

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

3. Calculate \( (4.5)^3 \):

\[ (4.5)^3 = 4.5 \times 4.5 \times 4.5 = 20.25 \times 4.5 = 91.125 \]

4. Now plug this value back into the volume formula:

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

5. First, calculate \( \frac{4}{3} \times 3.14 \):

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

6. Now, multiply this result by \( 91.125 \):

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

Thus, the volume of the basketball is approximately:

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