# A restaurant hall is 20m long, 15m wide and 10m high. The interior of the hall except the ceiling and the base has to be covered with bright wallpaper. What will be the total expenditure if the wallpaper costs Rs.60 per m^{2}?

Any solid with three dimensions, that is length, breadth and height is a cuboid.

## Answer: For a restaurant hall that is 20m long, 15m wide and 10m high, the total expenditure to cover the walls with wallpaper will cost Rs 42,000.

For any cuboid with dimensions: length (l), breadth (b), and height (h), the total surface area of cuboid is given as 2(lb + bh + hl).

**Explanation:**

Given the dimensions of the restaurant hall:

Length, l = 20m

Breadth, b = 15m

Height, h = 10m

Since the interior of the hall except the ceiling and the base are covered with wallpaper, this means the wallpaper is covering the entire surface area of the restaurant hall except for the ceiling and the floor

Let's find the total area covered by the wallpaper first:

The total area covered by the wallpaper = Total surface area of all the faces of the restaurant hall - Surface area of the ceiling part and the Base

Total surface area of all the faces of the restaurant hall = Total surface area of the rectangle = 2(lb + bh + hl) = 2(20×15 + 15×10 + 10×20) = 2 (300 + 150 + 200) = 2 × 650 = 1300 square metres.

The surface area of the ceiling part = Surface area of the rectangle that forms the ceiling part = l × b = 20 × 15 = 300 m^{2 }

Surface area of the ceiling = Surface area of the base = 300 m^{2}

Now, the total area covered by the wallpaper = 1300 - (300 + 300) = 700 m^{2}.

Now, if the wallpaper costs Rs 60 per m^{2}, then the total cost of the wallpaper is:

Area to be covered by wallpaper × Cost of the wallpaper per square

= 700 × 60 = Rs 42,000

### Therefore, the total expenditure on the wallpaper is Rs 42,000.

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