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Find the lateral surface area of a cuboid whose length,breadth,and height are in the ratio of 4:3:2 and volume of the cuboid is 5184 m cube.




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Given the ratio of the length, breadth and height = 4:3:2
Let the length be 4x m 
breadth be 3x m 
height be 2x m
The volume of the cuboid is given as 5184m³
⇒4x* 3x* 2x = 5184m²
⇒24x³ = 5184
⇒x³ = 5184/24
⇒x = ∛216
⇒x = 6
 ∴Length = 4x = 4* 6 = 24m
Breadth = 3x = 3*6 = 18m
Height = 2x = 2*6 = 12m
Lateral surface area of a cuboid = 2(l + b) h
⇒2(24m + 18m)12m
⇒84m* 12m = 1008m²
2 4 2
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