A chest made

A chest in the shape of a cuboid made of sheet iron has dimensions of 2.4 m × 0.8 m × 0.5 m. What will be the volume of a cube-shaped chest with the same surface area?

Final Answer:

V₂ =  34.186 m³

Step-by-step explanation:

$$\begin{gathered} a=24\doteq 3.2455\text{m} \\ b=0.8\text{m} \\ c=0.5\text{m} \\ S=2\cdot (a\cdot b+b\cdot c+c\cdot a)=2\cdot (3.2455\cdot 0.8+0.8\cdot 0.5+0.5\cdot 3.2455)=\frac{316}{5}=63.2{\text{m}}^2 \\ S=S \\ S=6a^2 \\ a=\sqrt{S/6}=\sqrt{63.2/6}\doteq 3.2455\text{m} \\ {V}_2=a^3=3.2455^3=34.186{\text{m}}^3 \end{gathered}$$

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