# 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:

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

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Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

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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