Question

Pyramid A is a square pyramid with a base side length of 14 inches and a height of 6 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.

Answer 1

The Volume of PYRAMID A is 8 times greater than the Volume of PYRAMID B as obtained by taking the ratio of the volume of both pyramids.

Volume of a square based pyramid is given as :

$V = a^2h/3$

Where; h = height ; a = base edge

Hence, Volume of PYRAMID A :

$V = 14^2 * (6/3)\\\\V = 392 in^3$

Volume of PYRAMID B = 3,136 in³

Divide Volume of pyramid B by pyramid A :

$3136 in^3 / 392 in^3$

= 8 times

Expressing as a percentage, multiply by 100% ;

8 * 100% = 800%

Therefore, The volume of PYRAMID B is 800% times GREATER THAN that of PYRAMID A.

Learn more :

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Answer 2

Answer:

r = 8  ( The volume of pyramid B is 8 times bigger than the volume of pyramid A

As percentage

The volume of pyramid B is 800 % bigger than the volume of pyramid A

Step-by-step explanation:

The volume for a right square pyramid is:

V = (1/3) * x²*h        where  x is the side of the square base and h the height, according to this: the volume of pyramid A is:

V(A) = (1/3)* (14)²*6 = 392 in³

Pyramid B has a volume of  3136 in³.

For us to get how many times the volume of pyramid B is bigger than the volume of pyramid A, we divide

r = Volume of pyramid B / Volume of pyramid A

r = 3136/ 392

r = 8

As percentage volume of pyramid B is 800 % bigger than the volume of pyramid A