The cheerleaders are making buttons for homecoming. They are printing paper circles with a diameter of 3 inches that will be folded over a metal backing and covered with clear plastic. If a 1/2 inch border is folded over, how much of the picture will show on the finished button.
(Use 3.14 for pi)
R = 1.5
r = 1
pi R^2 - pi r^2
pi (1.5)^2 - pi (1)^2
I got 6.565in^2
pi (2.25 -1) = 1.25 pi = 3.93
oh thanks
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To find out how much of the picture will show on the finished button, we need to calculate the area of the paper circle and subtract the area of the folded border.
Step 1: Calculate the area of the paper circle.
The formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius.
Given that the diameter of the circle is 3 inches, the radius (r) is half the diameter, which is 3/2 = 1.5 inches.
Using the formula, we can calculate the area of the paper circle:
A = π(1.5)^2
A = 3.14(1.5)^2
A = 3.14 * 2.25
A = 7.065 square inches
Step 2: Calculate the area of the folded border.
The diameter of the folded border is the diameter of the paper circle minus the folded portion, which is 1/2 inch.
So the diameter of the border is 3 inches (diameter of paper) - 1/2 inch (folded border) = 2.5 inches.
The radius (r) of the border is half the diameter, which is 2.5/2 = 1.25 inches.
Using the formula, we can calculate the area of the border circle:
A = π(1.25)^2
A = 3.14 * 1.5625
A ≈ 4.90875 square inches
Step 3: Calculate the area of the picture that will show on the finished button.
The area of the picture that will show on the finished button is the area of the paper circle minus the area of the folded border.
Area of picture = Area of paper circle - Area of border
Area of picture = 7.065 square inches - 4.90875 square inches
Area of picture = 2.15625 square inches
Therefore, approximately 2.15625 square inches of the picture will show on the finished button.