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.
