The problem states that a ball has a radius of 5 inches. Each pump adds 16 cubic inches of air to the ball. We need to find out how many pumps it will take to completely fill the empty ball, rounding the answer to the nearest tenth.

1. Problem Description

The problem states that a ball has a radius of 5 inches. Each pump adds 16 cubic inches of air to the ball. We need to find out how many pumps it will take to completely fill the empty ball, rounding the answer to the nearest tenth.

2. Solution Steps

First, we need to calculate the volume of the ball. The formula for the volume of a sphere is:

$V = \frac{4}{3}\pi r^3$

where $V$ is the volume and $r$ is the radius.

We are given that the radius $r = 5$ inches. Substituting this value into the formula, we get:

$V = \frac{4}{3} \pi (5^3)$

$V = \frac{4}{3} \pi (125)$

$V = \frac{500}{3} \pi$

Using the approximation $\pi \approx 3.14159$, we have:

$V \approx \frac{500}{3} (3.14159)$

$V \approx 523.5987756$ cubic inches

Next, we need to determine how many pumps are required to fill the ball. Each pump adds 16 cubic inches of air. To find the number of pumps needed, we divide the total volume by the volume added per pump:

Number of pumps $= \frac{\text{Total Volume}}{\text{Volume per pump}}$

Number of pumps $= \frac{523.5987756}{16}$

Number of pumps $\approx 32.72492347$

Finally, we need to round the answer to the nearest tenth:

Number of pumps $\approx 32.7$

3. Final Answer

It will take approximately 32.7 pumps to completely fill the empty ball.