# 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

Result

a =  6 cm
b =  9 cm
c =  15 cm

#### Solution:

$a=2x \ \\ b=3x \ \\ c=5x \ \\ \ \\ V=810 \ \text{cm}^3 \ \\ V=abc=2 \cdot \ 3 \cdot \ 5 \ x^3 \ \\ \ \\ x=\sqrt[3]{ V/(2 \cdot \ 3 \cdot \ 5)}=\sqrt[3]{ 810/(2 \cdot \ 3 \cdot \ 5)}=3 \ \text{cm} \ \\ \ \\ a=2 \cdot \ x=2 \cdot \ 3=6 \ \text{cm}$
$b=3 \cdot \ x=3 \cdot \ 3=9 \ \text{cm}$
$c=5 \cdot \ x=5 \cdot \ 3=15 \ \text{cm}$

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