# Cuboid - edges

The cuboid has dimensions in ratio 4: 3: 5, the shortest edge is 12 cm long. Find:
(A) the lengths of the remaining edges,
(B) the surface of the cuboid,
(C) the volume of the cuboid

Result

a =  16 cm
c =  20 cm
S =  1504 cm2
V =  3840 cm3

#### Solution:

$b=12 \ \\ k=b/3=12/3=4 \ \\ a=4 \cdot \ k=4 \cdot \ 4=16 \ \text{cm}$
$c=5 \cdot \ k=5 \cdot \ 4=20 \ \text{cm}$
$S=2 \cdot \ (a \cdot \ b+b \cdot \ c+a \cdot \ c)=2 \cdot \ (16 \cdot \ 12+12 \cdot \ 20+16 \cdot \ 20)=1504 \ \text{cm}^2$
$V=a \cdot \ b \cdot \ c=16 \cdot \ 12 \cdot \ 20=3840 \ \text{cm}^3$

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