Pyramid A is a square pyramid with a base side length of 18 inches and a height of 9 inches. Pyramid B has a volume of 3,136 cubic inches. How many times bigger is the volume of pyramid B than pyramid A? Give your answer as a percentage. Provide an explanation and proof for your answer to receive full credit.

Explained below, let me know if you need further explanation or proof.

Step-by-step explanation:We know the volume of B so done there, now let's find the volume of A

The volume of a pyramid (or cone) is (1/3)*l*w*h or (1/3)*A*h where A is the volume of the base.  If you need to prove that let me know

Pyramid A has a square base, area of a square is one side multiplied by another, but a square specifically has sides that are the same length, so you only need to do a side squared, or in other words multiplied by itself.  h is height, so A  has a height of 8 and side lengths of the base of 12.  so the volume is (1/3)*12*12*8

So now you have volume of angle A (I will call A) and volume of angle B (I will call B).  It wants to know now how many times larger B than A.  well "times larger" means multiplication.  if it were just "how much larger" you might use addition.  Anyway, this is asking how much do we have to multiply A by to get B.  so we will call this multiplying number x  so just use algebra to solve Ax = B for x.  

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146%

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