Question

Calculate the volume of a sphere that has a diameter of 7 inches. Use 3.14 for pi and round to the nearest tenth.(1 point) inches3

Answer 1

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

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

where \( V \) is the volume and \( r \) is the radius of the sphere. First, we need to find the radius from the diameter.

Given that the diameter is 7 inches, the radius \( r \) is:

\[
r = \frac{\text{diameter}}{2} = \frac{7}{2} = 3.5 \text{ inches}
\]

Now we can substitute \( r \) and \( \pi \) (approximated as 3.14) into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times (3.5)^3
\]

First, calculate \( (3.5)^3 \):

\[
(3.5)^3 = 3.5 \times 3.5 \times 3.5 = 12.25 \times 3.5 = 42.875
\]

Now substitute this value into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times 42.875
\]

Calculate \( 3.14 \times 42.875 \):

\[
3.14 \times 42.875 \approx 134.2855
\]

Now multiply by \( \frac{4}{3} \):

\[
V \approx \frac{4}{3} \times 134.2855 \approx 178.714
\]

Finally, rounding to the nearest tenth:

\[
V \approx 178.7 \text{ inches}^3
\]

Thus, the volume of the sphere is approximately \( \boxed{178.7} \) inches³.