The dimensions of the cuboid are in the ratio of 4:3:2 if the total surface area of the cuboid is 4212 meter sq.find the volume of the cuboid

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Solution

Ratio of l:b:h=4:3:2
Let l=4x m b=3x m h = 2x m
Total surface area = 4212sq m 2(lb+bh+lh)=4212 2(4x3x+3x2x+2x4x)= 4212 2(12x^2+6x^2+8x^2)=4212 226x^2=4212 x^2=4212/(226)
After cancellation x^2 =81 x^2 = 9^2 x=9
Therefore l=4x =49=36m b=3x =39=27m h=2x =29= 18m
Volume of a cuboid = lbh = 36m 27m 18m =17496 m^3

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