Question

reasoning the volume of a new extra - large toy tennis ball for pets is about 221 cubic centimeters. if 3 extra - large toy tennis balls are packaged and sold in a cylindrical package, what is the approximate volume of the cylindrical package? round to the nearest cubic centimeter. explain. round each answer to the nearest hundredth, if necessary.

Explanation:

Step1: Recall volume - ball and cylinder relationship

The volume of a sphere (tennis - ball) is given by $V_{sphere}=\frac{4}{3}\pi r^{3}$, and the volume of a cylinder with the same radius $r$ and height $h$ is $V_{cylinder}=\pi r^{2}h$. When three spheres are stacked in a cylinder, the height of the cylinder $h = 6r$ (since the diameter of a sphere is $2r$ and there are 3 spheres).

Step2: Given volume of one ball

We know that the volume of one ball $V_{sphere}=\frac{4}{3}\pi r^{3}=221$ cubic centimeters.

Step3: Find the volume of the cylinder

The volume of the cylinder $V_{cylinder}=\pi r^{2}h$. Since $h = 6r$, then $V_{cylinder}=\pi r^{2}(6r)=6\pi r^{3}$.
We know that $\frac{4}{3}\pi r^{3}=221$, so $\pi r^{3}=\frac{3\times221}{4}$.
Substitute $\pi r^{3}$ into the cylinder - volume formula: $V_{cylinder}=6\times\frac{3\times221}{4}$.
$V_{cylinder}=\frac{6\times3\times221}{4}=\frac{3978}{4}=994.5\approx995$ cubic centimeters.

Answer:

995