Question

The dimensions of a cuboid are in the ratio 1:2:3& its total surface area is 198 m2. find the area of its base​

Answer 1

Given :

• The dimensions of a cuboid are in the ratio 1:2:3
• Its total surface area is 198 m².

To find :

• The area of its base =?

Step-by-step explanation :

Let, the length of the cuboid =x, breadth =2x, height =3x

Total surface area of a cuboid =2(l×b+b×h+l×h)

Given, total surface area of the cuboid = 198 m²

⇒ 2(x×2x+2x×3x+x×3x) = 198

⇒ 22x² = 198

⇒ x² = 198/22

⇒ x² = 9

⇒ x = 3

Hence, the length of the cuboid = x = 3m, breadth =3x = 6m, height = 3x = 9m.

Now,

Area of cuboid base = Area of Rectangle = length x breadth.

Substituting the values, we get,

= 3 × 6

= 24.

Hence, the area of base of cuboid = 24m².