A wooden pyramid, 3 inches tall, has a square base. A carpenter increases the dimensions of the wooden pyramid by a factor of 6 and makes a larger pyramid with the new dimensions. Describe in complete sentences the ratio of the volumes of the two pyramids.

thanks for any help!

Question

A wooden pyramid, 3 inches tall, has a square base. A carpenter increases the dimensions of the wooden pyramid by a factor of 6 and makes a larger pyramid with the new dimensions. Describe in complete sentences the ratio of the volumes of the two pyramids.

thanks for any help!

directrix · Answer

The scale factor of the original pyramid to the enlarged pyramid is 1 to 6 or 1/6.

The ratio of the volumes of the two pyramids is the cube of the scale factor.

The ratio of the volumes is 1 : 216 or 1/216 meaning that the enlarged pyramid has 216 times the capacity of the original one.