Rectangular cuboid

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

Result

V =  23519.015 cm3

Solution:

$a = 2 \ x \ \\ b = 4 \ x \ \\ c = 5 \ x \ \\ S = 5334 \ cm^2 \ \\ \ \\ S = 2(ab+bc+ac) = 2(2 \cdot \ 4 \ x^2 + 4 \cdot \ 5 \ x^2 + 2 \cdot \ 5 \ x^2) \ \\ S = 76 \ x^2 \ \\ \ \\ x = \sqrt{ S / 76 } = \sqrt{ 5334 / 76 } \doteq 8.3776 \ cm \ \\ \ \\ a = 2 \cdot \ x = 2 \cdot \ 8.3776 \doteq 16.7552 \ cm \ \\ b = 4 \cdot \ x = 4 \cdot \ 8.3776 \doteq 33.5104 \ cm \ \\ c = 5 \cdot \ x = 5 \cdot \ 8.3776 \doteq 41.888 \ cm \ \\ \ \\ V = a \cdot \ b \cdot \ c = 16.7552 \cdot \ 33.5104 \cdot \ 41.888 \doteq 23519.0145 = 23519.015 \ cm^3$

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Amy
Not very useful plz give worked example with steps

2 years ago  2 Likes
Dr Math
Example is complete with solution  step-by-step

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