Question

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

Answer 1

Step-by-step explanation:

The total surface area of cuboid = 2(l × b + b × h + h × l)

Volume of cuboid = l × b × h

Where l → Length of cuboid

b → Breath of cuboid

h → Height of cuboid

Calculation:

Let the length, breath and height be 6x, 5x, and 3x respectively.

The total surface area of cuboid = 504 cm2

⇒ 2(l × b + b × h + h × l) = 504

⇒ 6x × 5x + 5x × 3x + 3x × 6x = 252

⇒ 30x2 + 15x2 + 18x2 = 252

⇒ 63x2 = 252

⇒ x2 = 4

⇒ x = 2

Length of the cuboid = 6x

⇒ 6 × 2

⇒ 12 cm

Breath of the cuboid = 5x

⇒ 5 × 2

⇒ 10 cm

Height of the cuboid = 3x

⇒ 3 × 2

⇒ 6 cm

Volume of cuboid = l × b × h

⇒ 12 × 10 × 6

⇒ 720 cu cm

∴ The volume of the cuboid is 720 cu cm.