Question

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. the volume of a new extra - large toy tennis ball for pets is about 221 cubic centimeters. explain. round each answer to the nearest hundredth, if necessary. substitute 221 for v in the formula v=\frac{4}{3}pi r^{3}. 528=\frac{4}{3}pi r^{3}, so 132=\frac{1}{3}pi r^{3} and rapprox3.17. the base of the cylindrical package will have a radius equal to that of the tennis ball, or 3.17 cm. the height of the package will equal the diameter of three tennis balls, or 3(2)(3.17)=19.02 cm. the package is v = pi r^{2}h. v=pi(3.17)^{2}(19.02) or about 591 cubic centimeters.

Explanation:

Step1: Recall volume formula for sphere

The volume of a sphere is $V=\frac{4}{3}\pi r^{3}$. Given $V = 221\ cm^{3}$, we have $221=\frac{4}{3}\pi r^{3}$. Solving for $r^{3}$, we get $r^{3}=\frac{221\times3}{4\pi}$. Then $r^{3}=\frac{663}{4\pi}\approx\frac{663}{4\times3.14}\approx52.8$. So $r\approx\sqrt[3]{52.8}\approx3.75\ cm$.

Step2: Determine height and radius of cylinder

The height $h$ of the cylindrical package is equal to the diameter of three tennis - balls, so $h = 6r$. Substituting $r\approx3.75\ cm$, we get $h=6\times3.75 = 22.5\ cm$. The radius $R$ of the base of the cylindrical package is equal to the radius of a tennis - ball, so $R = r\approx3.75\ cm$.

Step3: Recall volume formula for cylinder

The volume formula for a cylinder is $V_{cylinder}=\pi R^{2}h$. Substituting $R = 3.75\ cm$ and $h = 22.5\ cm$ into the formula, we have $V_{cylinder}=\pi\times(3.75)^{2}\times22.5=\pi\times14.0625\times22.5\approx3.14\times14.0625\times22.5 = 3.14\times316.40625\approx993\ cm^{3}$.

Answer:

$993\ cm^{3}$