6. You are given a sheet of cardboard that is 8.0 in. x 11.0 in. How many full circles with a diameter of 3.0 inches can you cut from the cardboard? What is the percentage of waste if the
a. At =8*11= 88 in^2 = Total area.
Ac = pi*r^2 = 3.14 * 1.5^2 = 7.07 in^2. = Area of each circle.
As = 3 * 3 = 9 in^2. = Area of a 3 in square in which the circle can be inscribed.
At/As = 88/9 = 9.78 or 9 = The number of squares = the number of circles that can be cut.
b. 9Ac Aw= 88.
63.63 + Aw = 88, Aw = 24.37 in^2 = Area wasted.
%Waste = (24.37/88)*100% = 27.7
It would help if you proofread your questions before you posted them. "if the...?"
6 3-inch diameter circles can be cut within a 6 by 9 inch sheet.
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To find the number of full circles that can be cut from the cardboard, we need to determine how many circles with a diameter of 3.0 inches can fit within the dimensions of the cardboard.
The diameter of the circle is 3.0 inches, which means the radius (half the diameter) is 1.5 inches.
The length of the cardboard is 8.0 inches, and the width is 11.0 inches.
To calculate how many circles fit in the length-wise direction, we divide the length of the cardboard by the diameter of the circle:
Number of circles in length = length of cardboard / diameter of circle
Number of circles in length = 8.0 inches / 3.0 inches
Number of circles in length ≈ 2.67 circles
Since we cannot have a fraction of a circle, we round down to the nearest whole number. Therefore, we can fit 2 circles in the length-wise direction.
To calculate how many circles fit in the width-wise direction, we divide the width of the cardboard by the diameter of the circle:
Number of circles in width = width of cardboard / diameter of circle
Number of circles in width = 11.0 inches / 3.0 inches
Number of circles in width ≈ 3.67 circles
Again, rounding down to the nearest whole number, we can fit 3 circles in the width-wise direction.
To find the total number of circles that can be cut from the cardboard, we multiply the number of circles in the length-wise direction by the number of circles in the width-wise direction:
Total number of circles = number of circles in length x number of circles in width
Total number of circles = 2 circles x 3 circles
Total number of circles = 6 circles
Therefore, you can cut 6 full circles with a diameter of 3.0 inches from the given sheet of cardboard.
Now, to find the percentage of waste, we need to calculate the leftover area after cutting out the circles.
The area of each circle is given by the formula:
Area of a circle = π * (radius)^2
Area of a circle = 3.14 * (1.5 inches)^2
Area of a circle ≈ 7.06 square inches
To find the total area of the circles cut out, we multiply the area of a single circle by the total number of circles:
Total area of the circles = area of a circle x total number of circles
Total area of the circles = 7.06 square inches x 6 circles
Total area of the circles ≈ 42.36 square inches
The total area of the cardboard is given by multiplying the length and width:
Total area of the cardboard = length of cardboard x width of cardboard
Total area of the cardboard = 8.0 inches x 11.0 inches
Total area of the cardboard = 88 square inches
To find the waste percentage, we divide the total area of waste (leftover cardboard) by the total area of the cardboard and multiply by 100:
Waste percentage = (total area of cardboard - total area of the circles) / total area of the cardboard * 100
Waste percentage = (88 square inches - 42.36 square inches) / 88 square inches * 100
Waste percentage ≈ 51.36% waste
Therefore, the waste percentage is approximately 51.36%.