Question

find the volume of a basketball with a diameter of 9.2 inches, use 3.14 for pi and round to the nearest hundredth

Answer 1

The formula to calculate 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 from the diameter:

\[
\text{Diameter} = 9.2 \text{ inches} \implies \text{Radius} = \frac{9.2}{2} = 4.6 \text{ inches}
\]

Next, we can substitute the radius and \( \pi \) into the volume formula:

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

Now, we calculate \( (4.6)^3 \):

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

Now substitute this value into the volume formula:

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

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

\[
\frac{4}{3} \times 3.14 \approx 4.1867
\]

Now, calculate the volume:

\[
V \approx 4.1867 \times 97.336 \approx 408.6462
\]

Finally, rounding to the nearest hundredth:

\[
V \approx 408.65 \text{ cubic inches}
\]

Thus, the volume of the basketball is approximately **408.65 cubic inches**.