the ratio of length, breadth and height of a cuboid is 5: 3: 2 and the total surface area of it is 3968cm sq , find the dimension of the cuboid.
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Kind of a fun question because you’re starting with area which is a square and then converting a to a cubic. Surface area of a cuboid is basically 2 of each rectangle created by the measurements sides. The sides are created by taking the missing factor (x) in the 5:4:2 proportion, solve for x and you have the lengths and then the volume is easy.
2(2x*4x + 2x*5x + 4x*5x) = 1216 cm^2
8x^2 + 10x^2 + 20x^2 = 608 cm^2
38x^2 = 608 cm^2
x^2 = 16 cm^2
x=4 cm
8 cm * 16 cm * 20 cm = 2560 cm^3
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