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29 July, 09:14

What is the length of diagonal d of a cube that is 10 on each edge? Round your answer to the nearest tenth of an inch.

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  1. 29 July, 12:25
    0
    17.3 in

    Step-by-step explanation:

    (a) Diagonal on a face

    First, we calculate the diagonal f on a face of the cube.

    a² + a² = f²

    f² = 2a²

    (b) Diagonal of the cube

    Consider the triangle made by the diagonal d, diagonal f, and the edge of the cube

    d² = f² + a²

    Substitute the value of f² d² = 2a² + a² = 3a²

    Take the square root of each side d = a√3

    Substitute the value of a d = 10√3 = 10 * 1.732 = 17.3 in

    The diagonal of the cube is 17.3 in.
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