Rectangular cuboid

The rectangular cuboid has a surface area 5334 cm², and its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.

Correct result:

V =  23519.0145 cm³

Solution:

$$\begin{gathered} a=2x \\ b=4x \\ c=5x \\ S=5334{\text{cm}}^2 \\ S=2(ab+bc+ac)=2(2\cdot 4x^2+4\cdot 5x^2+2\cdot 5x^2) \\ S=76x^2 \\ x=\sqrt{S\mathrm{/}76}=\sqrt{5334\mathrm{/}76}\doteq 8.3776\text{ cm } \\ a=2\cdot x=2\cdot 8.3776\doteq 16.7552\text{ cm } \\ b=4\cdot x=4\cdot 8.3776\doteq 33.5104\text{ cm } \\ c=5\cdot x=5\cdot 8.3776\doteq 41.888\text{ cm } \\ V=a\cdot b\cdot c=16.7552\cdot 33.5104\cdot 41.888=23519.0145{\text{cm}}^3=2.352\cdot 10^4{\text{cm}}^3 \end{gathered}$$

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Showing 2 comments:

Amy

Not very useful plz give worked example with steps

3 years ago  2 Likes Like

Dr Math

Example is complete with solution  step-by-step

2 years ago  Like

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