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24 September, 10:56

Find the volume of a regular tetrahedron whose altitude measures 10cm.

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  1. 24 September, 10:57
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    H = 10 cm, a - edge;

    V = 1/3 a²√3 / 4 * h

    h² = (2/3 * a√3 / 2) ² + a²

    100 = a²/3 + a²

    100 = 4 a² / 3

    a² = 75

    a = √75

    a = 5 √3 cm

    V = 1/2 * 75√3 / 4 * 10 = 250√3 / 4 = 62.5√3 cm³ ≈ 108.25 cm³
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