Painting a room: the area of four walls
Your family wants to paint a room before Tihar. Change the room's length, breadth and height and the price of paint, find the area of the four walls and the cost, and see why the walls unroll into one long rectangle.
Core concept
The four walls of a cuboid room unroll into one rectangle 2(l + b) long and h high, so their area is 2h(l + b); the floor is l × b, and the cost is the area × the rate
Topic: Area and volume
A room is shaped like a cuboid: length l, breadth b and height h. It has two walls l long and two walls b long, all h high. If you could unroll the four walls into one strip, the strip would be as long as the distance round the floor, 2(l + b), and as high as the room. So the area: How much flat space a shape covers, measured in square units like cm². All key words of the four walls is 2h(l + b). The floor (and the ceiling) is l × b. Painters charge by the square metre, so the cost of painting is the area × the rate in rupees per m².
What you will learn
- Find the area of the four walls of a room using 2h(l + b).
- Find the area of the floor and the ceiling of a room.
- Work out the cost of painting or carpeting from an area and a rate.
Before you start
- Know how to find the area and perimeter of a rectangle.
Materials
- A measuring tape and a notebook
Equipment
- A shoebox to model a room
Procedure
- Record a room 5 m × 4 m × 3 m with paint at Rs 100 per m².
- Make the room 4 m high and record.
- Change the paint to Rs 150 per m² and record.
- Record a room 6 m × 3 m × 3 m and compare it with the first.
How this simulation is simplified
- The room is a cuboid, and the doors and windows are painted over too (we ignore them).