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