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18 May, 11:27

Pyramid A is a square pyramid with a base side length of 12 inches and a height of 6 inches. Pyramid B has a volume of 2,880 cubic inches. How many times bigger is the volume of pyramid B than pyramid A? Give your answer as a percent. Provide an explanation and proof for your answer to receive full credit.

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  1. 18 May, 15:09
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    The Volume of Pyramid B is 10 times bigger that the Volume of Pyramid A.

    Also, expressing our answer in percent (percentage format), the Volume of Pyramid B is 90 percent (90%) bigger than Pyramid A.

    Step-by-step explanation:

    We have two pyramids.

    Pyramid A

    We are given base side length = 12 inches

    Height = 6 inches

    The formula for the Volume of a Square Pyramid is

    Volume = a² h / 3

    where a = base side length or base side edge

    h = height of the pyramid.

    Therefore, Volume of pyramid A is calculated as:

    = (12² * 6) : 3

    = 864 : 3

    = 288 cubic inches.

    Therefore, the Volume of Pyramid A = 288 cubic inches.

    In the question, we are given the Volume of Pyramid B = 2880 cubic inches

    And we are asked to find how many times bigger the Volume of Pyramid B is compared to Pyramid A.

    Volume of Pyramid A = 288 cubic inches

    Volume of Pyramid B = 2800 cubic inches.

    This is calculated as:

    Pyramid B : Pyramid A

    = 2880 cubic inches : 288 cubic inches

    = 10

    This means Pyramid B is 10 times bigger than Pyramid A.

    In the question, we are asked to express our answer in percent

    This is calculated as:

    = [ (Volume of Pyramid B - Volume of Pyramid A) : Volume of Pyramid B ] * 100

    = [ (2880 - 288) : 2880] * 100

    = (2592 : 2880) * 100

    = 0.9 * 100

    = 90%.

    Therefore, expressing our answer in percent, the Volume of Pyramid B is 90% bigger than the Volume of Pyramid A.
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