Question

Tennis balls are sold in cylindrical cans with the balls stacked one on top of the other. A tennis ball has a diameter of 6.7 cm. To the nearest cubic centimeter, what is the minimum volume of the can that holds a stack of 4 tennis balls?

Answer 1

To find the volume of the can, we need to find the total volume taken up by 4 tennis balls and add some extra volume to account for the empty space in the can.

The volume of one tennis ball can be calculated using the formula for the volume of a sphere: V = (4/3) * π * r^3, where r is the radius of the ball (which is half of the diameter).

Plugging in the values, we get:
V = (4/3) * π * (3.35)^3 ≈ 179.56 cm^3

The total volume taken up by 4 tennis balls is:
4 * 179.56 ≈ 718.24 cm^3

Now, since the tennis balls are stacked one on top of the other, there will be some empty space between the balls and at the top of the can. To approximate this, we can assume that the 4 tennis balls are arranged as tightly packed as possible, in a configuration similar to a pyramid. We can divide the total volume by 2 to find the minimum volume of the can:

718.24 / 2 ≈ 359.12 cm^3

Therefore, to the nearest cubic centimeter, the minimum volume of the can that holds a stack of 4 tennis balls is approximately 359 cm^3.