Question

A wooden pyramid, 9 inches tall, has a square base. A carpenter increases the dimensions of the wooden pyramid by a factor of 4 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's use a cube.
E.g.: I have a 2x2x2 cube, and I (the cool carpenter) increase the dimension by 7
My cube's dimensions would be 14*14*14

Okay, my old cube's volume is 2*2*2 which is 2^3 = 8
Now my NEW cube is 14^3 = 2744

And NOTICE that 8 x 7^3 = is equal to 2744 too! :D

Thus, we can conclude that, if the dimension of a solid is increased by x, it's area ratio would be increased of x^2, and the volume ratio x^3.