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 inches cubed 381.5 in.3 381.5 inches cubed 113 in.3 113 inches cubed 3,052.1 in.3

Answer 1

To find the volume of a basketball, we use the formula for the volume of a sphere:

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

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

1. First, calculate the radius from the diameter:

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

2. Using the approximation \( \pi \approx 3.14 \), substitute \( r \) 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 substitute this value back into the volume formula:

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

5. Calculate \( \frac{4}{3} \times 3.14 \):

   \[ \frac{4}{3} \times 3.14 \approx 4.18667 \text{ (approximately, but we can continue using the fraction)} \]

6. Now multiply by \( 91.125 \):

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

So the volume of the basketball is approximately \( 381.5 \) cubic inches.

Thus, the answer is \( \text{381.5 inches cubed} \).