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 find out how much air the exercise ball can hold when pumped to maximum capacity, we need to calculate the volume of the sphere (the shape of the exercise ball). The formula for the volume \( V \) of a sphere is given by:

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

Where \( r \) is the radius of the sphere.

1. **Calculate the radius**:
The diameter of the exercise ball is 20 inches. Therefore, the radius \( r \) is half of the diameter:

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

2. **Plug the radius into the volume formula**:
Now we substitute the radius into the volume formula using \( \pi \approx 3.14 \):

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

First, calculate \( (10)^3 \):

\[
(10)^3 = 1000
\]

Now substitute this value back into the volume formula:

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

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

\[
= \frac{12.56}{3} \approx 4.18666667
\]

Now multiply this by 1000:

\[
V \approx 4.18666667 \times 1000 \approx 4186.66667
\]

3. **Round to the nearest tenth**:
Rounding \( 4186.66667 \) to the nearest tenth gives us:

\[
V \approx 4186.7 \text{ inches}^3
\]

Thus, the volume of air the exercise ball can hold when pumped to its maximum capacity is approximately **4186.7 inches³**.