# Uboid volume

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

Result

V =  210 cm3

#### Solution:

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

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