The area of a circle 200mm in diameter is approximately how many times greater than the area of a circle 40mm in diameter?
A = pi * r^2
A = 3.14 * 100^2
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A = 3.14 * 20^2
502.4
To compare the areas of the two circles, we need to calculate the ratio of their areas.
1. First, let's find the area of the circle with a diameter of 200mm.
Area of a circle = π * (radius)^2
Radius = diameter / 2
Radius = 200mm / 2 = 100mm
Area of the circle = π * (100mm)^2
2. Now, let's find the area of the circle with a diameter of 40mm.
Radius = 40mm / 2 = 20mm
Area of the circle = π * (20mm)^2
3. To find the ratio of the areas, divide the area of the larger circle by the area of the smaller circle:
Ratio = (π * (100mm)^2) / (π * (20mm)^2)
The π (pi) term cancels out, simplifying the ratio to:
Ratio = (100mm)^2 / (20mm)^2
Simplifying further:
Ratio = 10000mm^2 / 400mm^2
The mm^2 (square millimeter) units also cancel out, leaving us with:
Ratio = 10000 / 400
Calculating the ratio:
Ratio = 25
Therefore, the area of the circle with a diameter of 200mm is approximately 25 times greater than the area of the circle with a diameter of 40mm.
To find the ratio of the areas of two circles, one with a diameter of 200mm and the other with a diameter of 40mm, we need to use the formula for the area of a circle.
The area of a circle is given by the formula:
A = πr^2
Where A is the area and r is the radius of the circle.
To find the radius of each circle, we divide the diameter by 2:
For the circle with a diameter of 200mm, the radius (r) is 200mm/2 = 100mm
For the circle with a diameter of 40mm, the radius (r) is 40mm/2 = 20mm
Now, we can calculate the areas of the two circles.
For the circle with a radius of 100mm:
A1 = π(100mm)^2
For the circle with a radius of 20mm:
A2 = π(20mm)^2
To compare the area of the first circle to the second circle, we can calculate the ratio:
A1/A2 = [π(100mm)^2] / [π(20mm)^2]
Notice that the π (pi) cancels out:
A1/A2 = (100mm)^2 / (20mm)^2
Simplifying this ratio, we get:
A1/A2 = (100/20)^2 = 5^2 = 25
Therefore, the area of a circle with a diameter of 200mm is approximately 25 times greater than the area of a circle with a diameter of 40mm.