woo9dlehelokie woo9dlehelokie

29-09-2016
Mathematics

Answered

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

Verified Answer :

HomertheGenius HomertheGenius

30-09-2016

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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