Uboid volume

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

Result

V =  210 cm3

Solution:

S1=ab=30 S2=bc=35 S3=ac=42  V=abc S1 S2 S3=ab bc ac=a2 b2 c2 S1 S2 S3=(abc)2=V2  V=S1 S2 S3 V=30 35 42=210 cm3S_{ 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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