Cuboid and ratio

Cuboid has dimensions in ratio 1:2:6 and the surface area of the cuboid is 1000 dm². Calculate the volume of the cuboid.

Correct answer:

V =  1500 dm³

Step-by-step explanation:

$$\begin{gathered} V=abc \\ a:b:c=1:2:6 \\ a=1k \\ b=2k \\ c=6k \\ S=1000 \\ S=2(ab+bc+ac) \\ S=2(2k^2+12k^2+6k^2)=40k^2 \\ k=\sqrt{S\mathrm{/}40}=\sqrt{1000\mathrm{/}40}=5 \\ a=k=5 \\ b=2\cdot k=2\cdot 5=10 \\ c=6\cdot k=6\cdot 5=30 \\ V=a\cdot b\cdot c=5\cdot 10\cdot 30=1500{\text{dm}}^3 \end{gathered}$$

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