# Uboid volume

Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²

Result

V =  210 cm3

#### Solution:

$S_{ 1 } = ab = 30 \ \\ S_{ 2 } = bc = 35 \ \\ S_{ 3 } = ac = 42 \ \\ \ \\ V = abc \ \\ S_{ 1 } \cdot \ S_{ 2 } \cdot \ S_{ 3 } = ab \cdot \ bc \cdot \ ac = a^2 \cdot \ b^2 \cdot \ c^2 \ \\ S_{ 1 } \cdot \ S_{ 2 } \cdot \ S_{ 3 } = (abc)^2 = V^2 \ \\ \ \\ V = \sqrt{ S_{ 1 } \cdot \ S_{ 2 } \cdot \ S_{ 3 } } \ \\ V = \sqrt{ 30 \cdot \ 35 \cdot \ 42 } = 210 = 210 \ cm^3$

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