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)

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1 answer

To calculate the volume of the exercise ball when it is fully inflated, we can use the formula for the volume of a sphere:

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

Given that the diameter of the ball is 20 inches, we can find the radius by dividing the diameter by 2:

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

Now, we can plug the radius 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 that back into the volume formula:

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

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

\[ \frac{4 \times 3.14}{3} = \frac{12.56}{3} \approx 4.1866667 \]

Now we can multiply that by 1000:

\[ V \approx 4.1866667 \times 1000 \approx 4186.6667 \]

Finally, rounding to the nearest tenth:

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

So, the exercise ball can hold approximately 4186.7 inches³ of air when pumped to maximum capacity.