Find the volume of a cuboid …

Surface Area of a cuboid = 104 sqcm (given)

Ratio of L : B : H = 2 : 3 : 4 

Let's assume L = 2x, B = 3x & H = 4x

We know, Surface Area of a cuboid  = 2 (lb + bh + lh) = 2 (2x*3x + 3x*4x + 4x*2x) = 2 (6x² + 12x² + 8x²) = 2 (26x²) = 52x²

52x² = 104 => x² =  2 => x =  √2

Now the volume of Cuboid = lbh = 2x * 3x * 4x = 24x³ = 24 * (√2)³ = 24 * 2 * √2 = 48√2 cubiccm (Answer)

Ans. As ratio is given 2:3:4

Total Surface Area of Cuboid = 104 cm²

Let Length of Cuboid = 2x

Breadth of Cuboid = 3x

Height of Cuboid = 4x

We Know

\(TSA = 2 [lh + lb + bh]\)

=> \(104 = 2[2x\times 3x + 2x\times 4x + 3x\times 4x]\)

=> \(52 = [6x^2 + 8x^2 + 12x^2]\)

=> \(52 = 26x^2\)

=> \(x^2 = 2 \)

=> \(x = \sqrt 2\)

So Length = \(2\sqrt 2\)

Breadth = \(3\sqrt 2\)

Height = \(4\sqrt 2\)

Volume of cuboid = \(2\sqrt 2 \times 3\sqrt 2 \times 4\sqrt 2 = 48\sqrt 2cm^3\)