Cuboid and ratio

Find the dimensions of a cuboid having a volume of 810 cm³ if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5

Correct answer:

a =  6 cm
b =  9 cm
c =  15 cm

Step-by-step explanation:

$$\begin{gathered} a=2x \\ b=3x \\ c=5x \\ V=810{\text{cm}}^3 \\ V=abc=2\cdot 3\cdot 5x^3 \\ x=\sqrt[3]{V\mathrm{/}(2\cdot 3\cdot 5)}=\sqrt[3]{810\mathrm{/}(2\cdot 3\cdot 5)}=3\text{ cm } \\ a=2\cdot x=2\cdot 3=6\text{ cm} \end{gathered}$$

$b=3\cdot x=3\cdot 3=9\text{ cm}$

$c=5\cdot x=5\cdot 3=15\text{ cm}$

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