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.

____ inches^3

Answer 1

To find the volume of the exercise ball, we can use the formula for the volume of a sphere, which is given by:

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

where \( V \) is the volume, \( \pi \) is approximately 3.14, and \( r \) is the radius of the sphere.

First, we need to determine the radius from the diameter. The diameter of the exercise ball is given as 20 inches. The radius is half of the diameter:

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

Now, we can substitute the radius into the volume formula:

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

Calculating \( (10)^3 \):

\[
(10)^3 = 1000
\]

Now, substituting into the volume formula:

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

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

\[
\frac{4000}{3} \approx 1333.3333
\]

Now, multiplying by \( 3.14 \):

\[
V \approx 1333.3333 \times 3.14 \approx 4186.6666
\]

Finally, rounding to the nearest tenth:

\[
V \approx 4186.7
\]

Thus, the volume of air that the exercise ball can hold when pumped to maximum capacity is approximately:

\[
\boxed{4186.7 \text{ inches}^3}
\]