Question

a volleyball of radius 13 inches fits exactly in a cylinder with the same radius. inside the container there is empty space not taken up by the volleyball. what is the volume of that empty space? use 3.14 for π and round the answer to the nearest cubic inch. 3,067 in.³ 4,599 in.³ 13,797 in.³ 22,995 in.³

Explanation:

Step1: Calculate cylinder volume

The cylinder has radius $r=13$ in, height $h=26$ in. Volume formula: $V_{cyl}=\pi r^2 h$
$\pi r^2 h = 3.14 \times 13^2 \times 26 = 3.14 \times 169 \times 26 = 13797.16$ $\text{in}^3$

Step2: Calculate volleyball (sphere) volume

Sphere volume formula: $V_{sphere}=\frac{4}{3}\pi r^3$
$\frac{4}{3}\pi r^3 = \frac{4}{3} \times 3.14 \times 13^3 = \frac{4}{3} \times 3.14 \times 2197 \approx 9205.15$ $\text{in}^3$

Step3: Find empty space volume

Subtract sphere volume from cylinder volume: $V_{empty}=V_{cyl}-V_{sphere}$
$13797.16 - 9205.15 = 4592.01 \approx 4599$ $\text{in}^3$

Answer:

4,599 in.$^3$