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. substitute 221 for v in the formula v = \frac{4}{3}\pi r^{3}, = \frac{4}{3}\pi r^{3}, so 52.8 \approx r^{3} and r \approx. the base of the cylindrical package will have a radius equal to that of the tennis ball, or cm. the height of the package will equal the diameter of three tennis balls, or 32() = 3() or cm. so, the volume of the package is v = \pi()^{2}() or about cubic centimeters.

Explanation:

Step1: Find the radius of the tennis - ball

Given the volume formula of a sphere $V=\frac{4}{3}\pi r^{3}$, and $V = 221$. Substitute $V$ into the formula: $221=\frac{4}{3}\pi r^{3}$. Then $r^{3}=\frac{221\times3}{4\pi}=\frac{663}{4\pi}\approx52.8$. So $r=\sqrt[3]{52.8}\approx3.75$ cm.

Step2: Determine the dimensions of the cylinder

The radius of the base of the cylindrical package $r_{cylinder}=r_{ball}\approx3.75$ cm. The height of the cylindrical package $h = 3\times(2r)=6r$. Substituting $r\approx3.75$ cm, we get $h = 6\times3.75 = 22.5$ cm.

Step3: Calculate the volume of the cylinder

The volume formula of a cylinder is $V=\pi r^{2}h$. Substitute $r = 3.75$ cm and $h = 22.5$ cm into the formula: $V=\pi\times(3.75)^{2}\times22.5=\pi\times14.0625\times22.5\approx994$ $cm^{3}$.

Answer:

994