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

Correct answer:

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

Step-by-step explanation:

$$\begin{gathered} b=12 \\ k=b/3=12/3=4 \\ a=4\cdot k=4\cdot 4=16\text{cm} \end{gathered}$$

$c=5\cdot k=5\cdot 4=20\text{cm}$

$S=2\cdot (a\cdot b+b\cdot c+a\cdot c)=2\cdot (16\cdot 12+12\cdot 20+16\cdot 20)=1504{\text{cm}}^2$

$V=a\cdot b\cdot c=16\cdot 12\cdot 20=3840{\text{cm}}^3$

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