Answer to Question #333352 in Geometry for Tsyan

Question #333352

A piece of steel is in the form of a tetrahedron whose base is a right-angled triangle. The sides forming the right-angle are 5 cm and 6 cm long respectively. If the height of the tetrahedron is 7 cm, calculate its volume. If the tetrahedron is melted down, calculate the length of bar of diameter 20 mm that can be made from it, assuming no waste.


1
Expert's answer
2022-04-26T00:03:45-0400


Known: AB = 5cm, BC = 6cm, htetrahedron = 7cm, d = 20mm

Vtetrahedron=1/3 S*h, where

S = SABC = AB*BC/2, and h - height, h = 7, then

"V_{tetrahedron} = \\frac{AB*BC*h}{6}\\\\\nV_{tetrahedron} = \\frac{5\\times6\\times7}{6} = 35 cm^3, then\\\\\nV_{tetrahedron} = 35000 mm^3"


"V_{bar} = V_{cylinder} = \\pi R^2 h, where R = d\/2, then\\\\\nV_{bar} = \\frac{\\pi d^2h}{2^2}, hence\\;\\\\\nh = \\frac{4V}{\\pi d^2}, then \\,\nh = \\frac{4\\times35000}{\\pi\\times20^2}=111.4mm"

Answer: the length of bar = 111.4mm or 11.14 cm


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