Question

Raphael wants to purchase an exercise ball. The dimensions state that the ball is 20 inches in diameter when at maximum capacity. How much air can the exercise ball hold when pumped to the maximum capacity? Calculate your answer using 3.14 for pi and round to the nearest tenth.(1 point) inches3

Answer 1

To calculate the volume of the exercise ball, we will use the formula for the volume \( V \) of a sphere, which 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. The diameter of the exercise ball is 20 inches, so the radius \( r \) can be calculated as follows:

\[
r = \frac{diameter}{2} = \frac{20 \text{ inches}}{2} = 10 \text{ inches}
\]

Now we can substitute the radius and the value of \( \pi \) into the volume formula. Using \( \pi \approx 3.14 \):

\[
V = \frac{4}{3} \times 3.14 \times (10)^3
\]

Calculating \( (10)^3 \):

\[
(10)^3 = 1000
\]

Now substituting this back into the equation:

\[
V = \frac{4}{3} \times 3.14 \times 1000
\]

Calculating \( \frac{4}{3} \times 1000 \):

\[
\frac{4}{3} \times 1000 \approx 1333.33
\]

Now we multiply this result by \( 3.14 \):

\[
V \approx 1333.33 \times 3.14 \approx 4187.9992
\]

Rounding to the nearest tenth:

\[
V \approx 4188.0
\]

Therefore, the exercise ball can hold approximately **4188.0 cubic inches** of air when pumped to maximum capacity.