Question

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

Answer 1

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