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The corresponding edges of two regular tetrahedrons are 1 cm and 3 cm. If the sum of the weights of the two tetrahedrons is 100 grams and both solids are made up of the same material, find the weight of the bigger solid.

Verified Answer :

HomertheGenius

m 1 = V 1 d
m 2 = V 2 d
Both tetrahedrons have the same density.
V = 1/3 a²√3/4 h
V 1 = 1/3 1² √3 / 4 √2 / √3 = √2 / 12 cm³ 
V 2 = 1/3 3²√3 /4  √6 = 9√2 / 4 cm³
m 1 : m 2 = √2 /12 : 9√2/4
m 1 9√2 / 4 = m 2  √2 / 12
m 1 = m 2 / 27
m 1 + m 2 = 100 g
m 2 / 27 + m 2 = 100 g   / 27
m 2 + 27 m 2 = 2700
28 m 2 = 2700
m 2 = 2700 : 28
m 2 = 96.42 g
Answer:
The weight of the bigger tetrahedron is 96.42 g. 

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