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4 May, 17:32

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.

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  1. 4 May, 18:28
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    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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