Question

tim bought some tennis balls packaged in a cylindrical tube. the tube has a radius of 1.4 inches and a height of 11 inches. the tube contains 4 spherical tennis balls that each have a radius of 1.35 inches. the remaining space in the tube is filled by pressurized air. what is the volume of space in the tube filled by pressurized air? round your answer to the nearest tenth. cubic inches

Explanation:

Step1: Calculate the volume of the cylindrical tube

The formula for the volume of a cylinder is $V_{cylinder}=\pi r^{2}h$.
Given $r = 1.4$ inches and $h=11$ inches.
$V_{cylinder}=\pi\times(1.4)^{2}\times11=\pi\times1.96\times11 = 21.56\pi\approx21.56\times3.14 = 67.7$ cubic inches.

Step2: Calculate the volume of one spherical tennis - ball

The formula for the volume of a sphere is $V_{sphere}=\frac{4}{3}\pi r^{3}$.
Given $r = 1.35$ inches.
$V_{sphere}=\frac{4}{3}\pi\times(1.35)^{3}=\frac{4}{3}\pi\times2.460375=3.2805\pi\approx3.2805\times3.14 = 10.3$ cubic inches.

Step3: Calculate the volume of 4 spherical tennis - balls

$V_{4 - spheres}=4\times V_{sphere}$.
$V_{4 - spheres}=4\times10.3 = 41.2$ cubic inches.

Step4: Calculate the volume of the pressurized air

The volume of the pressurized air $V = V_{cylinder}-V_{4 - spheres}$.
$V=67.7 - 41.2=26.5$ cubic inches.

Answer:

$26.5$ cubic inches