Uboid volume

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

Correct answer:

V =  210 cm³

Step-by-step explanation:

$$\begin{gathered} S_1=ab=30 \\ {S}_2=bc=35 \\ {S}_3=ac=42 \\ V=abc \\ {S}_1\cdot S_2\cdot S_3=ab\cdot bc\cdot ac=a^2\cdot b^2\cdot c^2 \\ {S}_1\cdot S_2\cdot S_3=(abc{)}^2=V^2 \\ V=\sqrt{S_1\cdot S_2\cdot S_3} \\ V=\sqrt{30\cdot 35\cdot 42}=210{\text{cm}}^3 \end{gathered}$$

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