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.

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.