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 cm2  S=2(ab+bc+ac)=2(2⋅ 4 x2+4⋅ 5 x2+2⋅ 5 x2) S=76 x2  x=S/76=5334/76≐8.3776 cm  a=2⋅ x=2⋅ 8.3776≐16.7552 cm b=4⋅ x=4⋅ 8.3776≐33.5104 cm c=5⋅ x=5⋅ 8.3776≐41.888 cm  V=a⋅ b⋅ c=16.7552⋅ 33.5104⋅ 41.888≐23519.0145≐23519.015 cm3a=2 \ x \ \\ b=4 \ x \ \\ c=5 \ x \ \\ S=5334 \ \text{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 \ \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 \doteq 23519.0145 \doteq 23519.015 \ \text{cm}^3

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Showing 2 comments:
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Amy
Not very useful plz give worked example with steps

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

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