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.

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.

campbell_st · Answer

the ratio of lengths is 1:6

the ratio of base area is 1:36

this can be shown if the base side length is 1 unit then Area = 1 unit^2
 increasign by  a factor of 6          side length 6             Area = 36 units^2

with volume the lnear measurements are cubed    1:6  for volume is 1:216

the volume will be 216 times larger. 

using a square pyramid base length 1 unit height 3 units   V = 1/3 x 1^2 x 3

                                                                                                V = 1 unit^3

increasing all measurements by a factor of 6

                                                                                               V = 1/3x 6^2 x 18
                                                                                                V = 216 units^3