Answer:
Well first you would just have to look at the equation for the volume of a pyramid. This is:
V = (length * width * height) / 3
and so we can just say all pyramids have a volume of V.
So now we want the base to be 3 times bigger which means we would have to multiple the length and width by 3 and the new volume equation would be
V = (3*length * 3 * width * height) / 3
we can factor the two 3's from the parenthesis and get
V = 9(l * w * h) /3
if we are looking at a ratio of how much the volume increases we can say
aV = b(l * w * h) /3
since:
V = (l * w * h) / 3
then:
aV = bV, divide both sides by V and:
a = b
using this we can see that the volume increases by a factor of 9 for 3 times bigger
now for 6 times
V = (6 * l * 6 * w * h) / 3, pull 6 * 6 out
V = 36(l * w * h) /3
and this one increases by factor of 36
if we see a pattern it always increases by the square of the factor of the growoth of the base
so for 9 times bigger it would be 9^2 = 81
and for 27 times bigger it would be 27^2 = 729
Explanation: