Question

The length, breadth, and height of a cuboid are in the ratio 6: 5 : 3. If its total surface area is 504 cm², find its volume.

Answer 1

Let the length of the given cuboid = 6x

The breadth of the given cuboid = 5x

Height of the given cuboid = 3x

The total surface area of the given cuboid

= 2(lb + bh + hl)

= 2(`6x xx 5x + 5x xx 3x + 3x xx 6x`)

= (`30x^2 + 15x^2 + 18x^2`)

= `2 xx 63x^2 = 126x^2`

But, we are given total surface area = 504 cm²

∴ 126x² = 504

⇒ `x^2 = 504/126`

⇒ `x^2 = 4`

⇒ `x^2 = (2)^2`

⇒ x = 2 cm

∴ Length of the given cuboid = 6x

= `6 xx 2 "cm" = 12` cm

Breadth of the given cuboid = 5x

= `5 xx 2` cm = 10 cm

Height of the given cuboid = 3x

= `3 xx 2` cm = 6 cm

Now, volume of the cuboid = `l xx b xx h`

= `12 xx 10 xx 6 = 720` cm³