# 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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by malricky1

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by malricky1

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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

⇒2(42m)12m

⇒84m* 12m = 1008m²

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

⇒2(42m)12m

⇒84m* 12m = 1008m²