Question

1. the figure shows a can of three tennis balls. the can is just large enough so that the tennis balls will fit inside with the lid on. the diameter of each tennis ball is 1.7in. find the volume of the empty space. round final answer to the nearest hundredth. volume= type your answer.. cubic inches

Explanation:

Step1: Find radius of the ball

The diameter of each tennis ball is 1.7 in, so the radius $r = \frac{1.7}{2} = 0.85$ in.

Step2: Calculate height of the can

The can holds 3 stacked balls, so height $h = 3 \times 1.7 = 5.1$ in.

Step3: Calculate volume of the can

The can is a cylinder, volume formula: $V_{can} = \pi r^2 h$
$V_{can} = \pi \times (0.85)^2 \times 5.1 = \pi \times 0.7225 \times 5.1 \approx 11.58$ cubic inches

Step4: Calculate volume of one ball

Volume of a sphere: $V_{ball} = \frac{4}{3}\pi r^3$
$V_{ball} = \frac{4}{3}\pi \times (0.85)^3 = \frac{4}{3}\pi \times 0.614125 \approx 2.57$ cubic inches

Step5: Calculate total volume of 3 balls

$V_{total balls} = 3 \times 2.57 = 7.71$ cubic inches

Step6: Find empty space volume

Subtract total ball volume from can volume: $V_{empty} = V_{can} - V_{total balls}$
$V_{empty} = 11.58 - 7.71 = 3.87$ cubic inches

Answer:

3.87