# 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 result:

a =  16 cm
b =  32 cm
c =  48 cm

#### Solution:

$V=24576 \ \text{cm}^3 \ \\ a:b:C=2:4:6 \ \\ V=abc \ \\ V=2k \cdot \ 4k \cdot \ 6k=48k^3 \ \\ k=\sqrt[3]{ V/48}=\sqrt[3]{ 24576/48}=8 \ \text{cm} \ \\ a=2 \cdot \ k=2 \cdot \ 8=16 \ \text{cm}$
$b=4 \cdot \ k=4 \cdot \ 8=32 \ \text{cm}$
$c=6 \cdot \ k=6 \cdot \ 8=48 \ \text{cm}$

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