Cuboid - ratios

The sizes of the edges of the cuboid are in the ratio of 2:3:5. The smallest wall has an area of 54 cm². Calculate the surface area and volume of this cuboid.

Correct answer:

S =  558 cm²
V =  810 cm³

Step-by-step explanation:

$$\begin{gathered} a=2x \\ b=3x \\ c=5x \\ ab=54 \\ 6x^2=54 \\ x=\sqrt{54/6}=3 \\ a=2\cdot x=2\cdot 3=6 \\ b=3\cdot x=3\cdot 3=9 \\ c=5\cdot x=5\cdot 3=15 \\ {S}_1=a\cdot b=6\cdot 9=54 \\ {S}_2=b\cdot c=9\cdot 15=135 \\ {S}_3=a\cdot c=6\cdot 15=90 \\ S=2\cdot (S_1+S_2+S_3)=2\cdot (54+135+90)=558{\text{cm}}^2 \end{gathered}$$

$V=a\cdot b\cdot c=6\cdot 9\cdot 15=810{\text{cm}}^3$

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