A cuboidal hall is 15 m long and 10 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of the four walls, then the volume of the hall is:

Correct option is C

Given:

Length of the cuboidal hall = 15 m

Breadth of the cuboidal hall = 10 m

Formula Used:

Volume of cuboid;

Volume = Length × Breadth × Height

The areas involved are:

Area of the floor = Length × Breadth

Area of the ceiling = Length × Breadth

Area of the four walls = 2 × (Length × Height + Breadth × Height)

Solution:

Area of the floor + area of the ceiling = $$2 \times (15 \times 10)$$​ = 300 m²

Area of the four walls = 2 × (15 × h + 10 × h) = 2 × (15h + 10h) = 50h m²

The sum of the areas of the floor and the ceiling is equal to the sum of the areas of the four walls.

50h = 300

h = $$\frac{300}{50}$$​ = 6m

Now,

Volume = 15 × 10 × 6 = 900 m³