Question

Pólya's Principle Step 1: Understand the Problem 1. Describe in detail what you understand the problem to be. In other words, what problem will you need to solve? Is there enough information to enable you to find a solution to your problem? Show your work here: (10 points) 2. Discuss different ways to construct the room that will be painted. Are there any restrictions on where the window and door will be located? Will the overall amount of paint that is needed change based on where these are placed in the room? Show your work here: (10 points) 3. List the facts that you know. First, find the room dimensions in feet that make a good model for this situation. One strategy would be to sketch the room as follows. Please use this model to complete the following table below. (3 points) Side Answers Length Width 2 Helge 4. Using the measurements diagrammed above, label all of the rectangular faces in feet in the following table: (5 points) Face Dimensions Ceiling Page Dimensions Left W Right W Facemos Rack Wall

Answer 1

1)The problem is determine the dimensions of a room i.e it's length, breadth and height and the painting to be done which requires us to determine the surface area.Yes there is sufficient information.

2)The position of the door and windows can be changed depending on one's desire.Yes there are restrictions on the size of door ,they should not be too small so that the head does not hit the wall while entering.Even the size of window should be optimum to facilitate good air flow and ventilation.If the size of the door and window remains the same then the amount of paint required will be same as the surface area remains constant.

3. Length - 12ft
Width- 10ft
Height- 10ft

4)Ceiling - 12ft *10ft
Left wall -10ft *10ft
Right wall- 10ft *10ft
Front wall-12ft *10ft
Back wall-12ft *10ft
Height-10ft

5) Dimensions of the window on the back wall - 4ft*3ft.
3 feet and 9 inches is equal to 3.75 feet

6)The strategy is simple,we will use the conversion formula to convert inch to feet.To determine the area of the walls we will multiply the length and breadth or height depending on the wall.For painting we will subtract the areas of the door and window.

7. Considering that the door is of dimensions 7feet by 3feet, the front wall will have a surface area of ((12ft*10ft)-(7ft*3ft)) = 99 ft^2 which can be painted on.
Similarly the back wall with window will have a paint-able surface area of ((12ft*10ft)-(4ft*3ft)) = 108 ft^2.
The left and right walls have the same paint-able surface of 10ft*10ft = 100 ft^2.
The ceiling has a paint able surface of 12ft*10ft= 120 ft^2.

8)For two coat painting,

Left wall - 2*100 = 200 ft^2

Right wall - 2*100 = 200ft ^2

Front wall - 2*99 = 198 ft^2

Back wall - 2*108= 216ft^2

Ceiling - 2*120 = 240 ft^2