Hi im doing measurement at skool at the moment and i cant quite ork out some questions. Can someone please help!!
A metal washer has an external diameter of 2cm and an internal diameter of 1cm.
A) How many washers can be cut from a sheet of steel 3m by 1m?
B)If the metal left over was remelted and cast into a sheet of the same thickness and width 1m, how many additional washers could be cut?
A) If the washers are cut in a square array, you can get 100/2 = 50 per mm for a total of 150 x 50 or 7500 washers. You can get even more with a hexagonal close packed array. (Try it with pennies). In this case. the distance between rows is D*(sqrt3)/2 = 1.732 cm and you can get 57.7 rows per m, or 173 rows in 3 meters with alternately 50 or 49 per m, for a total ofN = 173 x 49.5 or 8563.
B) Calculate the volume of N washers (not counting the holes!) and divide that into the volume of the sheet of steel.
Sure, I can help you with that! Let's break down the questions step-by-step.
A) How many washers can be cut from a sheet of steel 3m by 1m?
1. Start by calculating the area of the sheet of steel. The formula for calculating area is: Area = Length × Width.
Area = 3m × 1m = 3 square meters
2. Now, let's calculate the area of one washer. The formula for calculating the area of a washer is: Area = π × (External Radius^2 - Internal Radius^2).
External Radius = External Diameter ÷ 2 = 2cm ÷ 2 = 1cm
Internal Radius = Internal Diameter ÷ 2 = 1cm ÷ 2 = 0.5cm
External Radius^2 = 1cm × 1cm = 1 square centimeter
Internal Radius^2 = 0.5cm × 0.5cm = 0.25 square centimeter
Area = π × (1 square centimeter - 0.25 square centimeter) = π × 0.75 square centimeters
3. Since the unit of area for the sheet is square meters and the unit of area for the washer is square centimeters, we need to convert the sheet area to square centimeters.
3 square meters × 10,000 square centimeters/1 square meter = 30,000 square centimeters
4. Now, divide the total area of the sheet by the area of one washer to find the number of washers that can be cut.
Number of washers = 30,000 square centimeters ÷ (π × 0.75 square centimeters) ≈ 12,699.04 washers
Since you can't have a fraction of a washer, the maximum number of washers that can be cut from the sheet is 12,699 washers.
B) If the metal left over was remelted and cast into a sheet of the same thickness and width (1m), how many additional washers could be cut?
1. The remaining metal is equivalent to the area of the sheet minus the area of the washers that were already cut.
Remaining area = 30,000 square centimeters - (12,699 washers × π × 0.75 square centimeters) ≈ 5,018.53 square centimeters
2. Divide the remaining area by the area of one washer to find the number of additional washers that can be cut.
Number of additional washers = 5,018.53 square centimeters ÷ (π × 0.75 square centimeters) ≈ 2,131.59 washers
Since you can't have a fraction of a washer, the maximum number of additional washers that can be cut is 2,131 washers.
Please note that these calculations are approximate due to rounding.
Absolutely! I'd be happy to help you with your measurement questions.
To answer these questions, we need to understand how to calculate the area of a washer and the area of a sheet of steel.
A) To find out how many washers can be cut from a sheet of steel, we first need to calculate the area of one washer.
The formula for the area of a circle is A = πr^2, where A represents the area and r represents the radius of the circle.
In this case, we have the external diameter of 2cm, so the radius is half of that, which is 1cm. Therefore, the area of one washer is:
A_washer = π * (1cm)^2 = 3.14 cm^2 (rounded to two decimal places)
Now, let's calculate the area of the entire sheet of steel:
A_sheet = length * width = 3m * 1m = 3 square meters (m^2)
To find out how many washers can be cut from the sheet of steel, divide the area of the sheet by the area of one washer:
Number of washers = A_sheet / A_washer = 30000 cm^2 / 3.14 cm^2 = 9547 (rounded to the nearest whole number)
So, you can cut approximately 9547 washers from the given sheet of steel.
B) Now, let's focus on the second question. We have the leftover metal from the first scenario, which is then remelted and cast into a sheet of the same thickness and width, 1m.
To find out how many additional washers can be cut from this remelted metal sheet, we can use the same calculation as in part A.
First, let's determine the area of the remelted metal sheet:
A_remelted_sheet = length * width = 1m * 1m = 1 square meter (m^2)
Again, divide the area of the remelted sheet by the area of one washer:
Number of additional washers = A_remelted_sheet / A_washer = 10000 cm^2 / 3.14 cm^2 = 3184 (rounded to the nearest whole number)
Therefore, you can cut approximately 3184 additional washers from the remelted metal sheet.
I hope this helps you understand how to approach these measurement questions! If you have any further queries, feel free to ask.