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26 October, 12:50

A square pyramid and a cube have the same surface area. The length of each side of the base of the square pyramid is 10 feet. The width of the cube is 6 feet. What is the slant height of the square pyramid?

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  1. 26 October, 15:09
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    The answer to your question is 23.2 ft

    Step-by-step explanation:

    Data

    length square pyramid = 10 ft

    width of a cube = 6 ft

    height of the pyramid = ?

    The surface area is equal in both figures.

    Formula

    Surface area of a cube = 6a²

    Surface area of a square pyramid = ab + al = l x l + (l x h) / 2

    Process

    1. - Calculate the surface area of the cube

    Ac = 6 (6) ² = 6 (36)

    = 216 ft²

    2. - Substitute data in the square pyramid formula

    Ap = (10 x 10) + (10h) / 2

    3. - Equal both areas

    216 = 100 + 5h

    - Solve for h

    216 - 100 = 5h

    116 = 5h

    h = 116 / 5

    - Result

    h = 23.2 ft
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