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 is 1:3

the ratio of volumes can be found by  raising each value in the ratio to the power of 3

(1)^3 :(3)^3   = 1:27

a test.... height 6 and assume the square base has side length of 1 inch

$$V = 1/3 \times 1^2 \times 6$$

V = 2 inches^3

now with the dimensions tripled

h = 18 and square side length is 3

$$V  = 1/3 \times 3^2\times 18$$

V = 54 inches ^3

the ratio of the volumes is 2:54 or 1: 27

anonymous · Answer

Thanks!