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.

__ inches^3

Answer 1

To calculate the volume of a sphere, we use the formula:

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

where \( r \) is the radius of the sphere. Given that the diameter of the sphere is 5 inches, we can find the radius by dividing the diameter by 2:

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

Now, we substitute \( r \) and \( \pi \) (using 3.14) into the volume formula:

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

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

\[
(2.5)^3 = 2.5 \times 2.5 \times 2.5 = 6.25 \times 2.5 = 15.625
\]

Now we substitute this back into the volume formula:

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

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

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

Now multiply this by 15.625:

\[
V \approx 4.18667 \times 15.625 \approx 65.44504
\]

Finally, rounding to the nearest tenth, we have:

\[
V \approx 65.4 \text{ inches}^3
\]

Thus, the volume of the sphere is approximately:

\[
\boxed{65.4} \text{ inches}^3
\]