Cuboid - ratios

The sizes of the edges of the cuboid are in the ratio 2: 3: 5. The smallest wall have area 54 cm2. Calculate the surface area and volume of this cuboid.

Correct result:

S =  558 cm2
V =  810 cm3

Solution:

a=2x b=3x c=5x ab=54 6x2=54 x=54/6=3 a=2 x=2 3=6 b=3 x=3 3=9 c=5 x=5 3=15 S1=a b=6 9=54 S2=b c=9 15=135 S3=a c=6 15=90 S=2 (S1+S2+S3)=2 (54+135+90)=558 cm2
V=a b c=6 9 15=810 cm3



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