Question

comparing volumes
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.
photo by chiswick chap

Explanation:

1. Height comparison: The stacked coins on the right are slanted, so their total vertical height is shorter than the straight stack on the left.
2. Face area comparison: A coin's face area in a horizontal plane depends on its angle; the slanted coins have a smaller projected face area in the same horizontal plane as the straight coins.
3. Volume comparison: Both stacks have identical coins, same type and count. Volume is a property of the total material, which is unchanged by rearranging the coins.

Answer:

• The two stacks have equal volume.