Question

Calculate the volume of a sphere that has a diameter of 7 inches. Calculate your answer using 3.14 for pi and round to the nearest tenth.

Answer 1

To calculate the volume of a sphere, you can use the formula:

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

where \( V \) is the volume and \( r \) is the radius of the sphere.

First, find the radius from the diameter. The diameter is given as 7 inches, so the radius \( r \) is:

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

Now, substitute the radius into the volume formula. Using \( \pi \approx 3.14 \):

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

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

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

Next, substitute \( (3.5)^3 \) into the volume formula:

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

Now calculate \( \frac{4}{3} \times 3.14 \):

\[
\frac{4}{3} \times 3.14 \approx 4.18667 \quad (\text{approximately})
\]

Now, multiply this by \( 42.875 \):

\[
V \approx 4.18667 \times 42.875 \approx 179.5327
\]

Finally, round this to the nearest tenth:

\[
V \approx 179.5
\]

So, the volume of the sphere is approximately **179.5 cubic inches**.