# Mystery of stereometrie

Two regular tetrahedrons have surfaces 88 cm2 and 198 cm2. In what ratio is their volumes?

Write as a fraction and as a decimal rounded to 4 decimal places.

Result

p =  0.2963

#### Solution:

$S ~ a^2 \ \\ V ~ a^3 \ \\ \ \\ S_1 = k_1 a_1^2 = 88 \ \\ S_2 = k_1 a_2^2 = 198 \ \\ \ \\ a_1:a_2 = \sqrt{ S_1}:\sqrt{ S_2} = \sqrt{ 88:198 } \ \\ \ \\ V_1:V_2 = (a_1:a_2)^3 = (88:198)^{3/2} \ \\ V_1:V_2 = (\dfrac{4}{9})^{3/2} = (\dfrac{2}{3})^{3} = \dfrac{ 8}{27} \ \\ V_1:V_2 = 0.296296296296 \doteq 0.2963 \ \\$

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