Question

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.

Answer 1

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.