The length, breadth, and height of a cuboid are in the ratio 5 : 3: 2. If its volume is 240 cm^{3}; find its dimensions. Also, find the total surface area of the cuboid.

#### Solution

Let length of the given cuboid = 5x

Breadth of the given cuboid = 3x

Height of the given cuboid = 2x

Volume of the given cuboid = Length x Breadth x Height

= 5x x 3x x 2x = 30x^{3}

But we are given volume = 240 cm^{3}

30x^{3} = 240 cm^{3}

⇒ x^{3} = `240/30`

⇒ x^{3} = 8

⇒ x = `8^(1/3)`

⇒ x = `(2 xx 2 xx 2)^(1/3)`

⇒ x = 2 cm

Length of the given cube = 5x = 5 x 2 = 10 cm

Breadth of the given cube = 3x = 3 x 2 = 6 cm

Height of the given cube = 2x = 2 x 2 = 4cm

Total surface area of the given cuboid = 2(l x b + b x h + h x l)

= 2(10 x 6 + 6 x 4 + 4 x 10) = 2(60 + 24 + 40) = 2 x 124

= 248 cm^{2}