Tamika is helping her father make shelves measuring 12x16" how many can be cut from a 48x72" piece of plywood so there is no waste?
48/16 = 3
72/12 = 6
so I can draw 18 rectangles of 12 by 16 on a piece of 48 by 72
BUT, using a regular saw there will be a saw-cut waste and that changes the question.
I will assume your question is ignoring the sawdust.
To calculate the number of shelves that can be cut from the plywood without any waste, we need to find the maximum number of shelves that can be fitted both vertically and horizontally.
1. Determine the number of shelves that can be cut vertically:
- Divide the height of the plywood (72") by the height of each shelf (16"): 72 / 16 = 4.5 shelves vertically
We can only have a whole number of shelves, so we can fit a maximum of 4 shelves vertically.
2. Determine the number of shelves that can be cut horizontally:
- Divide the width of the plywood (48") by the width of each shelf (12"): 48 / 12 = 4 shelves horizontally
We can fit a maximum of 4 shelves horizontally.
3. Calculate the total number of shelves:
- Multiply the number of shelves vertically by the number of shelves horizontally: 4 shelves vertically * 4 shelves horizontally = 16 shelves in total
Therefore, Tamika and her father can cut a maximum of 16 shelves measuring 12x16" from the 48x72" piece of plywood without any waste.
To find out how many shelves can be cut from a 48x72" piece of plywood without any waste, we need to calculate the number of shelves that can fit within the given dimensions.
Step 1: Determine the size of each shelf
Since the shelves are 12x16" each, the area of one shelf can be calculated by multiplying the length by the width:
Shelf area = 12" x 16" = 192 square inches
Step 2: Calculate the total available area in the plywood
To determine the area of the entire 48x72" plywood, multiply the length by the width:
Plywood area = 48" x 72" = 3,456 square inches
Step 3: Divide the total plywood area by the shelf area
By dividing the total plywood area by the shelf area, we can determine the maximum number of shelves that can be cut without any waste:
Number of shelves = Plywood area / Shelf area = 3,456 square inches / 192 square inches = 18 shelves (rounded down)
Therefore, Tamika and her father can cut 18 shelves measuring 12x16" from the 48x72" piece of plywood without any waste.