Question

2 stacks of coins are shown. In the first stack, the coins are stacked straight up. In the second stack, the coins are stacked to the side.
Look at the two stacks of coins. Each stack contains the same type and number of coins.

Make a conjecture. How do the stacks compare? Check all that apply.

The two stacks are the same height.
The area of a coin face in one stack is the same as the area of a coin face that lies in the same horizontal plane.
The two stacks have equal volume.

Answer 1

All three statements are true.

- Same height: each coin contributes the same thickness (height) no matter how it is shifted sideways, so total height = number of coins × coin thickness in both stacks.
- Same face area in a given horizontal plane: a horizontal cut through a coin face meets the same circular face (same radius), so the area of the coin face in one stack equals the area of the coin face lying in that same horizontal plane in the other stack.
- Equal volume: both stacks contain the same number of identical coins (identical cylinders), so their total volumes are equal.