A wooden pyramid, 9 inches tall, has a square base. A carpenter increases the dimensions of the wooden pyramid by a factor of 4 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 scale factor 1/4. 
If two polyhedra are similar then the cube of their scale factor is the ratio of their volumes.
(1/4)^3 = V/ V' where V is the volume of the original pyramid and V' is the volume of the enlarged pyramid.
1/64 = V/V'
The volume of the new pyramid is 64 times that of the original one.

anonymous · Answer

thanks