Sum

The length, breadth, and height of a cuboid are in the ratio 5:4: 2. If the total surface area is 1216 cm^{2}, find dimensions of the solid.

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#### Solution

Let the Length, breadth, and height of the cuboid be 5x,4xand 2x respectively.

Total Surface Area(TSA) = (LB+BH+LH) =1216

⇒ (LB+BH+LH) = 608

⇒ [(5x × 4x) +(4x × 2x) +(5x × 2x) =608

⇒ [20x^{2} +8x^{2}+10x^{2}] =608

⇒ 38x^{2} = 608

⇒ x^{2} = `608/38`

⇒ x^{2} = 16

⇒ x = 4

The dimension of the cuboid is:

Length = 5x = 5(4) = 20cm

Breadth = 4x = 4(4) = 16cm

Height = 2x = 2(4) = 8cm

∴volume = (L×B×H)

⇒ Volume = 20 × 16 × 8

⇒ Volume = 2560cm^{2}

Concept: Surface Area of a Combination of Solids

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