The Problem:

The problem states that the length of a room is 2 times its breadth and 5 times its height. The volume of the room is given as 800 cubic meters. We need to find the cost of wallpapering the walls of the room at a rate of Rs5.50 per square meter.

Understanding the Problem:

To solve this problem, we need to find the dimensions of the room and then calculate the total area of the walls. Finally, we can find the cost of wallpapering the walls by multiplying the area by the cost per square meter.

Step 1: Finding the Dimensions of the Room:

Let's assume the breadth of the room is 'b' meters.

According to the problem, the length of the room is 2 times its breadth. So, the length will be 2b meters.

Similarly, the height of the room is 5 times its breadth. So, the height will be 5b meters.

Step 2: Calculating the Volume of the Room:

The volume of a rectangular room can be calculated by multiplying its length, breadth, and height.

Volume = Length × Breadth × Height

Given that the volume of the room is 800 cubic meters, we can write the equation as:

800 = 2b × b × 5b

Simplifying the equation:

800 = 10b³

Dividing both sides of the equation by 10:

80 = b³

Taking the cube root of both sides:

b = ∛80

b ≈ 4.306 meters

Therefore, the breadth of the room is approximately 4.306 meters.

Step 3: Finding the Length and Height of the Room:

Using the values of the breadth, we can calculate the length and height of the room.

Length = 2 × Breadth = 2 × 4.306 = 8.612 meters

Height = 5 × Breadth = 5 × 4.306 = 21.53 meters

Therefore, the length of the room is approximately 8.612 meters and the height is approximately 21.53 meters.

Step 4: Calculating the Area of the Walls:

To calculate the area of the walls, we need to find the sum of the areas of all four walls.

The area of each wall can be calculated by multiplying its length and height.

Area of a wall = Length × Height

Area of one wall = 8.612 × 21.53 = 185.4 square meters

Since there are four walls, the total area of the walls is:

Total area of walls = 4 × 185.4 = 741.6 square meters

Therefore, the total area of the walls is 741.6 square meters.

Step 5: Finding the Cost of Wallpapering:

To find the cost of wallpapering, we need to multiply the total area of the walls by the cost per square meter.

Cost of wallpapering = Total area of walls × Cost per square meter

Cost of wallpapering = 741.6 × Rs5.50 = Rs4082.80

Therefore, the cost of wallpapering the walls of the room at a rate of Rs5.50 per square meter is Rs4082.80.

Summary:

- The breadth