Sue has a plastic paperweight shaped like a rectangular pyramid. The volume is 120 cubic inches, the height is 6 inches, and the length is 10 inches. She has a gift box that is a rectangular prism with a base that is 6 inches by 10 inches. How tall must the box be for it to hold the pyramid?

Accepted Solution

The volume of the pyramid is given by:
Volume=120 in³
The volume of rectangular prism is:
let the height be x:
the volume will be:
volume=x×6×10=60x in².
Therefore for the box to hold the pyramid, the box must have the same volume as the pyramid. hence the height of the box that will hold the pyramid will be:
solving for x we get:
x=2 inches.
Therefore for the box to hold the pyramid, it should be 2 inches tall.