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mrs_skeptik
2 months ago
7

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.
Mathematics
1 answer:
Svet_ta [12.7K]2 months ago
4 0
M 1 = V 1 * d
m 2 = V 2 * d
Both tetrahedrons share the same density.
V = 1/3 * a²√3/4 * h
For V 1 = 1/3 * 1² * √3 / 4 * √2 / √3 = √2 / 12 cm³ 
For V 2 = 1/3 * 3²√3 /4 * √6 = 9√2 / 4 cm³
Relating m 1 and m 2: m 1: m 2 = √2 /12: 9√2/4
m 1 * 9√2 / 4 = m 2 * √2 / 12
m 1 = m 2 / 27
The total mass, m 1 + m 2 = 100 g
Thus, m 2 / 27 + m 2 = 100 g   / * 27
m 2 + 27 m 2 = 2700
This gives 28 m 2 = 2700
So, m 2 = 2700: 28
Finally, m 2 = 96.42 g
Response:
The bigger tetrahedron weighs 96.42 g.

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