Question

The length, breadth and height of a rectangular solid are in ratio 5:4:2. If its total surface area is
1216 cm2, find the volume of the solid.​

Answer 1

Given,

that the ratio in length, breadth and height of a rectangular solid = 5 : 4 : 2

Total surface area =1216 cm²

Let’s assume the length = 5x, breadth = 4x and height = 2x

Total surface area = 2[5x × 4x + 4x × 2x + 2x × 5x]

= 2[20x2 + 8x2 + 10x2 ]

= 2 × 38x²

= 76x²

So, 76x² = 1216

⇒ x² = 1216/76 = 16 = (4)²

∴ x = 4

Hence,

the dimensions of the rectangular solid are

Length = 5 × 4 = 20 cm

Breadth = 4 × 4 = 16 cm

Height = 2 × 4 = 8 cm

and volume = lbh = 20 × 16 × 8 = 2560 cm³

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