Surface of cuboid

Find the surface of the cuboid if its volume is 52.8 cm³ and the length of its two edges is 2 cm and 6 cm.

Correct result:

S =  94.4 cm²

Solution:

$$\begin{gathered} V=52.8{\text{cm}}^3 \\ a=2\text{ cm } \\ b=6\text{ cm } \\ {S}_1=a\cdot b=2\cdot 6=12{\text{cm}}^2 \\ c=V\mathrm{/}{S}_1=52.8\mathrm{/}12={\displaystyle \frac{22}{5}}=4{\displaystyle \frac{2}{5}}=4.4\text{ cm } \\ S=2\cdot (S_1+b\cdot c+a\cdot c)=2\cdot (12+6\cdot 4.4+2\cdot 4.4)={\displaystyle \frac{472}{5}}=94{\displaystyle \frac{2}{5}}={\displaystyle \frac{472}{5}}{\text{cm}}^2=94.4{\text{cm}}^2 \end{gathered}$$

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