Question

A tennis ball has a diameter of 2.5”. Find the total surface area of the smallest cylindrical can that can hold three tennis balls vertically (including the top and the bottom) around answer to the nearest hundredth. No pi in your answer.

Answer 1

For the cylinder to be able to contain the balls it has to have a radius equals to the radius of the ball, then the radius of the cylinder must be at least 1.25 inches. The height of the cylinder is 3 times the 'height' of each sphere, which is equal to the diameter of the sphere, the diamenter of a sphere is 2 times its radius then the height of the cylinder is h=6r = 7.5 inches.

Finally we apply the formula for the surface area of a cylinder:

`\begin{gathered} A=\text{ 2}\pi rh\text{ + 2}\pi r^2=\text{ 2}\pi\text{ (1.25 in }\cdot7.5in+(1.25in)^2)=68.72in^2 \\ \end{gathered}`