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31 August, 11:51

ABCDE is a square-based pyramid.

its base has side length 8cm and centre M.

Angle ECM = 72 degrees

Work out the volume of the pyramid.

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Answers (2)
  1. 31 August, 12:43
    0
    371 cm³

    Step-by-step explanation:

    Assuming the base is ABCD and tip is at E

    CM is half the diagonal

    Length of the diagonal 'd'

    d² = 8² + 8²

    d² = 128

    d = 8sqrt (3)

    CM = 4sqrt (2)

    EMC is a right angle triangle, where EM is the height of the pyramid.

    tan (72) = EM/CM

    EM = tan (72) * 4sqrt (2) = 17.41

    Volume of pyramid;

    V = ⅓ (base area) * height

    V = ⅓ (8²) * 17.41

    V = 371.4134868 cm³

    V = 371 cm³ (3sf)
  2. 31 August, 15:24
    0
    371.41 cm^3.

    Step-by-step explanation:

    The volume = 1/3 * area of the square base * height.

    The area of the square base = 8^2 = 64 cm^2.

    To find the height we need to consider the triangle ECM in which CM is the line between center M and C on the Base, and EM is the height of the triangle (which also = height of the pyramid).

    We use Pythagoras to find length of CM.

    CM^2 = 4^2 + 4^2 (because 4 is half of the side length of 8 cm).

    CM = √32 cm.

    Now tan 72 = height / CM = EM / CM

    tan 72 = EM / √32

    EM = √32 tan 72

    So the volume of the pyramid is 1/3 * 64 * √32 tan 72

    = 371.41 cm^3.
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