Cuboid edges in ratio

Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm³.

Correct answer:

a =  16 cm
b =  32 cm
c =  48 cm

Step-by-step explanation:

$$\begin{gathered} V=24576{\text{cm}}^3 \\ a:b:C=2:4:6 \\ V=abc \\ V=2k\cdot 4k\cdot 6k=48k^3 \\ k=\sqrt[3]{V\mathrm{/}48}=\sqrt[3]{24576\mathrm{/}48}=8\text{ cm } \\ a=2\cdot k=2\cdot 8=16\text{ cm} \end{gathered}$$

$b=4\cdot k=4\cdot 8=32\text{ cm}$

$c=6\cdot k=6\cdot 8=48\text{ cm}$

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