Question

Some racquet balls are sold in cylindrical cans of three balls. Each ball has a diameter of 2.25 inches. The can has a diameter of 2.25 inches and is 6.75 inches tall. Find the volume of the empty space in the can. Use 3.14 for p. Round to the nearest hundredth.

Answer 1

Volume of 1 ball = 4/3 π r³ = 4/3 (3.14) (2.25 ÷ 2)³ = 5.961 in³

Volume of 3 balls = 5.961 x 3 = 17.883 in³

Volume of cylinder = πr²h = (3.14) (2.25 ÷ 2)² (6.75) = 26.825 in³

Empty Space = 26.825 - 17.883 = 8.94 in³ (nearest hundredth)

Answer: 8.94 in³

Answer 2

In order to find the empty space we need to find the total space and the filled space.

The formula we use to find the volume of the cans or any cylinder is:
$\pi {r}^{2} h$
Plug in the givens:
$3.14 \times {1.125}^{2} \times 6.75$
Simplify:

$3.14 \times 1.265625 \times 6.75 = 26.824921875$

Now let's find the balls' volume. These cans can hold 3 balls:

$n \times \frac{4}{3} \pi {r}^{3} \\ \\ 3 \times \frac{4}{3} \times 3.14 \times {1.125}^{3}$
Take the cube:
$3 \times \frac{4}{3} \times 3.14 \times 1.423828125$
Solve:
$3 \times \frac{4}{3} \times 3.14 \times 1.423828125 = 17.88328125$
To find the empty space:
$26.824921875 - 17.88328125 = 8.941640625$
The empty space is 8.94 in3.