Circular discs of radius 3.5cm are to be cut from a rectangular sheet of cardboard measuring 50cm by 30cm. once the disc are cut out, the remaining parts of the sheet are waste.
A. how many disc can be cut from one sheet of cardboard?
B. If % waste = waste/total area x 100,calculate the percentage waste fo this sizeof cardboard sheet.
diameter = 2r
30/7 = 4
50/7 = 7
Area used = 28 * πr^2 = ?
Subtract ? from 50*30 for waste
To find the number of discs that can be cut from one sheet of cardboard, we need to calculate the maximum number of circles that can fit into the rectangular sheet without overlapping.
The area of each circular disc can be calculated using the formula: A = π * r^2, where A is the area and r is the radius.
Given that the radius of the disc is 3.5 cm, the area of one disc can be calculated as:
A = π * (3.5)^2 = 38.465 cm^2 (approx.)
Next, we find the area of the rectangular sheet of cardboard:
Area of rectangle = length * width = 50 cm * 30 cm = 1500 cm^2
Dividing the area of the rectangular sheet by the area of one disc will give us the number of discs that can be cut from one sheet:
Number of discs = Area of rectangle / Area of one disc = 1500 cm^2 / 38.465 cm^2 ≈ 38.96 discs
However, we cannot have a fraction of a disc, so we need to take the integer value. Therefore, the maximum number of discs that can be cut from one sheet of cardboard is 38.
To calculate the percentage waste, we need to determine the waste area. It is the difference between the area of the rectangular sheet and the combined area of all the discs cut.
The combined area of all the discs can be calculated as:
Area of all discs = Area of one disc * Number of discs = 38.465 cm^2 * 38 = 1464.47 cm^2 (approx.)
The waste area can be calculated as the difference between the area of the rectangle and the area of all the discs:
Waste area = Area of rectangle - Area of all discs = 1500 cm^2 - 1464.47 cm^2 ≈ 35.53 cm^2
To find the percentage waste, we need to calculate the ratio of the waste area to the total area of the rectangle and multiply it by 100:
Percentage waste = (Waste area / Area of rectangle) x 100 = (35.53 cm^2 / 1500 cm^2) x 100 ≈ 2.36%
Therefore, the percentage waste for this size of cardboard sheet is approximately 2.36%.