A wooden pyramid, 12 inches tall, has a square base. A carpenter increases the dimensions of the wooden pyramid by a factor of 5 and makes a larger pyramid with the new dimensions. Describe in complete sentences the ratio of the volumes of the two pyramids.

Question

directrix · Answer

The two pyramids are similar with a scale factor of 1 to 5 or 1/5. 
If two pyramids are similar, the ratio of their volumes is the cube of their scale factor ratio. (1/5)^3 = 1/125. The volume of the larger pyramid is 125 times the volume of the original pyramid.