A cylindrical can holds three equal-sized balls perfectly. Which is larger, the can's height or the can's circumference?

Let the ball's radius be R.

The can's height is 6R.
The can's circumference is 2 pi R.

2 pi = 6.283.. > 6

Therefore, _____

Great question, one of my favourites.

I used to bring a tennis-ball can into class and challenge my students to give me a solution and explanation verbally.

Thanks drwls for the reminder.

To determine which is larger, the can's height or circumference, we need to know the dimensions of the can. Specifically, we need to know the radius and height of the cylinder.

The circumference of a cylinder is the distance around the circular base, and can be calculated using the formula:

Circumference = 2 x π x radius

The height of the cylinder is the distance from the base to the top.

However, since the question mentions that three equal-sized balls fit perfectly in the can, we can make a few assumptions.

First, the balls are likely touching both the base and the side of the cylinder. This means the diameter of a ball is equal to the cylinder's radius.

Second, the three balls are stacked on top of each other without any gap or overlap. Hence, the height of the cylinder is equal to three times the diameter of a ball.

Given these assumptions, we can compare the height and the circumference of the cylinder.

So, which is larger?

If the height of the cylinder (3 x diameter) is greater than the circumference (2 x π x radius), then the cylinder's height is larger.
If the circumference (2 x π x radius) is greater than the height (3 x diameter), then the circumference is larger.

However, without knowing the specific measurements, we cannot definitively determine which is larger.