Use the formula for the volume of a sphere to find the volume of a basketball that has a diameter of 9.2 inches. Use 3. 14 as an approximation for pi and round your answer to the nearest hundredth, if necessary. (1 point)

115.55 in.3

3,260.11 in.3

1,222.54 in.³

407.51 in.3

1 answer

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.

First, calculate the radius of the basketball. The diameter is 9.2 inches, so the radius is:

\[ r = \frac{d}{2} = \frac{9.2}{2} = 4.6 \text{ inches} \]

Now, substitute the radius and \(\pi \approx 3.14\) into the volume formula:

\[ V = \frac{4}{3} \times 3.14 \times (4.6)^3 \]

Calculate \( (4.6)^3 \):

\[ (4.6)^3 = 97.336 \]

Next, plug this value back into the volume formula:

\[ V = \frac{4}{3} \times 3.14 \times 97.336 \]

Now calculate \( \frac{4}{3} \times 3.14\):

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

Next, multiply this by \( 97.336 \):

\[ V \approx 4.18667 \times 97.336 \approx 407.51 \]

Rounding to the nearest hundredth:

\[ V \approx 407.51 \text{ in}^3 \]

Thus, the volume of the basketball is approximately 407.51 in³.