The volume of a square pyramid is given by the formula V = 1/3hx^2 where h is the height of the pyramid and x is the length of one side of t

Question

The volume of a square pyramid is given by the formula V = 1/3hx^2 where h is the height of the pyramid and x is the length of one side of the base. A pyramid with a height of 15 ft has a volume of 2880 ft^3. What is the length of one side of the base?

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Melanie 3 weeks 2021-09-27T08:22:09+00:00 1 Answer 0

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    2021-09-27T08:24:01+00:00

    Answer: 24\ ft

    Step-by-step explanation:

    The exercise gives you the following formula:

    V = \frac{1}{3}hx^2

    Where “h” is the height of the square pyramid and “x” is the length of one side of the base.

    According to the data given, you know that:

    h=15\ ft\\\\V=2,880\ ft^3

    Therefore, you can subsitute these values into the formula:

    2,880\ ft^3= \frac{1}{3}(15\ ft)x^2

    Now, you need to solve for the “x” to calculate the length of one side of the square base of that pyramid.

    You get that this is:

    2,880\ ft^3= \frac{1}{3}(15\ ft)x^2\\\\2,880\ ft^3= (\frac{15\ ft}{3})x^2\\\\2,880\ ft^3=(5\ ft)x^2\\\\\frac{2,880\ ft^3}{5\ ft}=x^2\\\\\sqrt{576\ ft^2}=x\\\\x=24\ ft

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