Question

Use the formula for the volume of a sphere to find the volume of a basketball that has a diameter of 9.2inches. Use 3.14 as an approximation for pi and round your answer to the nearest hundredth, if necessary.

1,222.54
407.51
3,260.11
115.55

Answer 1

The formula for the volume \( V \) of a sphere is given by:

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

where \( r \) is the radius of the sphere.

First, we need to find the radius of the basketball. The diameter is given as 9.2 inches, so the radius \( r \) is half of the diameter:

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

Now we can plug the radius into the volume formula using \( \pi \approx 3.14 \):

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

Calculating \( (4.6)^3 \):

\[
(4.6)^3 = 4.6 \times 4.6 \times 4.6 = 97.336
\]

Now, substituting this back into the volume formula:

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

Calculating \( \frac{4}{3} \times 3.14 \):

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

Now multiply this by 97.336:

\[
V \approx 4.18667 \times 97.336 \approx 407.515
\]

Rounding to the nearest hundredth, we find:

\[
V \approx 407.51
\]

Therefore, the volume of the basketball is **407.51 cubic inches**, so the correct option is **407.51**.