Question

Calculate the volume of a sphere that has a diameter of 5 inches. Use 3.14 for pi and round to the nearest tenth

Answer 1

To calculate the volume \( V \) of a sphere, you can use the formula:

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

Where \( r \) is the radius of the sphere. The radius is half of the diameter.

Given that the diameter of the sphere is 5 inches, the radius \( r \) would be:

\[
r = \frac{5}{2} = 2.5 \text{ inches}
\]

Now, plug the radius into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times (2.5)^3
\]

First, calculate \( (2.5)^3 \):

\[
(2.5)^3 = 2.5 \times 2.5 \times 2.5 = 15.625
\]

Now, substitute \( 15.625 \) back into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times 15.625
\]

Next, calculate \( 3.14 \times 15.625 \):

\[
3.14 \times 15.625 = 49.0625
\]

Now, compute \( \frac{4}{3} \times 49.0625 \):

\[
V = \frac{4 \times 49.0625}{3} = \frac{196.25}{3} \approx 65.4167
\]

Finally, round \( 65.4167 \) to the nearest tenth:

\[
V \approx 65.4 \text{ cubic inches}
\]

Thus, the volume of the sphere is approximately **65.4 cubic inches**.