Hi, I have a quick question that needs to be answered:
If plywood came in pieces that measure 8feet by 4feet, how many pieces of plywood are need to cover the roof (which has a base of 42 feet and a height of 25 feet)?
I would also like to ask you is it possible that you explain in detail how you retrieved your answer so I can get why the answer to the problem resulted as so.
Thank you,
Beautiful
Do this with a piece of graph paper, draw a rectangle the size of the roof, then start fitting pieces (8x4) onto the roof graph to get it to fit with the minimum number of plywood pieces. You may have to cut a few pieces of the plywood.
I'm confused becuase first off graph paper is not that large and second off cut what
Scale the graph paper: let each unit be 1 ft.
Cut off some of the rectangles representing the plywood. Work this as you would a jigsaw puzzle.
To answer the question of how many pieces of plywood are needed to cover the roof, we can start by determining the total area of the roof and then calculating how many plywood pieces are required to cover that area.
The area of a rectangle can be calculated by multiplying its base (the longer side) by its height. In this case, the base of the roof is given as 42 feet and the height is given as 25 feet. So, the total area of the roof can be calculated as:
Area of the roof = base × height = 42 feet × 25 feet = 1050 square feet
Next, let's calculate the area that a single piece of plywood can cover. The plywood comes in pieces that measure 8 feet by 4 feet, so the area of one plywood piece can be calculated as:
Area of plywood piece = length × width = 8 feet × 4 feet = 32 square feet
To determine the number of plywood pieces needed, we can divide the total area of the roof by the area of one plywood piece:
Number of plywood pieces = Total roof area / Area of one plywood piece
Number of plywood pieces = 1050 square feet / 32 square feet
Number of plywood pieces ≈ 32.81
Since we cannot have a fraction of a plywood piece, we need to round up to the nearest whole number. Therefore, we would need a minimum of 33 pieces of plywood to cover the entire roof.
Now, let's discuss the method that was mentioned earlier involving graph paper. The idea of using graph paper is to create a scaled representation of the roof and the plywood pieces. By using this representation, you can visually arrange the plywood pieces on the graph paper to see how they fit and calculate the number required.
To do this, you would need a large sheet of graph paper or multiple sheets taped together. Each unit on the graph paper can represent 1 square foot (which you can calculate based on the dimensions of the graph paper). Then, you can draw a rectangle on the graph paper to represent the roof, with the dimensions of 42 feet by 25 feet.
After that, you can draw smaller rectangles on the graph paper to represent the individual plywood pieces, with dimensions of 8 feet by 4 feet. Now, start fitting these plywood piece rectangles onto the roof rectangle on the graph paper and try to minimize the number of plywood pieces needed. You may find that some plywood pieces need to be cut or adjusted to fit properly.
This visual method helps you visualize the arrangement of plywood pieces and determine how many would be needed. It is like solving a jigsaw puzzle, where each plywood piece represents a puzzle piece.
I hope this explanation helps you understand how to arrive at the answer and the potential method you can use to solve similar problems involving spatial arrangement.