Cuboid edges

Calculate the volume and surface of a cuboid whose edge lengths are in the ratio 2: 3: 4 and the longest edge measures 10cm.

Correct answer:

V =  375 cm³
S =  325 cm²

Step-by-step explanation:

$$\begin{gathered} a:b:c=2:3:4 \\ a<b<c \\ c=10\text{ cm } \\ c=4x \\ x=c\mathrm{/}4=10\mathrm{/}4={\displaystyle \frac{5}{2}}=2.5 \\ a=2\cdot x=2\cdot 2.5=5\text{ cm } \\ b=3\cdot x=3\cdot 2.5={\displaystyle \frac{15}{2}}=7.5\text{ cm } \\ V=a\cdot b\cdot c=5\cdot 7.5\cdot 10=375{\text{cm}}^3 \end{gathered}$$

$S=2\cdot (a\cdot b+b\cdot c+a\cdot c)=2\cdot (5\cdot 7.5+7.5\cdot 10+5\cdot 10)=325{\text{cm}}^2$

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