posted by Kayla on .
A wooden pyramid, 12 inches tall, has a square base. A carpenter increases the dimensions of the wooden pyramid by a factor of 5 and makes a larger pyramid with the new dimensions. Describe in complete sentences the ratio of the volumes of the two pyramids.
the actual values of the dimensions make no difference.
If the original base sides are s, the height is h, then the volume v is
v = 1/3 s^2 * h
now, multiply each dimension by 5 and your new volume V is
V = 1/3 (5s)^2 * (5h)
= 1/3 * 25s^2 * 5h
= 125 * 1/3 s^2 * h
or, 5^3 * v
scaling the dimensions of a figure by a factor of n means
area is scaled by n^2
volume is scaled by n^3