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

Question

campbell_st · Answer

the ratio of the linear measurements will be 1:3

the height of 6inches  will become 18 in the new pyramid. 

which volumes... the linear measurements will be cubed to get the ratio of the volumes

$$1^3 : 3^3$$

or 1: 27

so the larger pyramid with measurements 3 time the smaller will be 27 times larger. 

e.g. 

if the pyramid is 6 inches tall and the square base has side length 1 inch

V = 1/3 x 1^2 x 6

V = 2 cubic inches

larger.... height = 18 base side length 3

V = 1/3 x 3^2 x 18

V = 54 cubic inches

ratio of the volumes is 

2:54 or 1:27

anonymous · Answer

thanks