Question

The length, breadth and the height of a cuboid are in the ratio 5: 3: 2. If its volume is 360 cm', find its
dimensions. Also, find the total surface area of the cuboid.​

Answer 1

ANSWER

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 = 30x3

But we are given volume = 240 cm3

30x3 = 240 cm3

⇒ x3 = 240/30

⇒ x3 = 8

⇒ x = 8.1/3

⇒ x = (2 x 2 x 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 cm2