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 dimensions. Also, find the volume of the cuboid.

Answer 1

Let length of the cuboid = 6x

Breadth of the cuboid = 5x

Height of the cuboid = 3x

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

= 2(6x x 5x + 5x x 3x + 3x x 6x) = 2(30×2 + 15×2 + 18×2)

= 2 x 63×2 = 126x² 

But we are given total surface area of the given cuboid = 504 cm² 

Length of the cuboid = 6x = 6 x 2 = 12 cm 

Breadth of the cuboid = 5x = 5 x 2 = 10cm

Height of the cuboid = 3x = 3 x 2 = 6 cm

Volume of the cuboid = l x b x h = 12 x 10 x 6 = 720 cm³