Question

MATH WORD PROBLEM HELP?


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.

Answer 1

Let the square base has sides = 4. V = (1/3) (4x4)(6) = 32
Now increase dimensions by a factor of 3, or sides of base = 12, height = 18
V = (1/3)(12x12)(18) = 864 = 32 x 27 = 32 x 3^3

Theorem: for 2 similar pyramids, The ratio of two volumes is equal to the cubic of the ratio of two lengths.