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Questions and Answers
What is the relationship between the circumference and diameter of a circle?
What is the relationship between the circumference and diameter of a circle?
- Circumference = $\frac{1}{2}$ Diameter
- Circumference = $\pi$ Diameter
- Circumference = Diameter
- Circumference = $2\pi$ Diameter (correct)
What is the formula for finding the area of a circle?
What is the formula for finding the area of a circle?
- $A = 2 \pi r$
- $A = \frac{1}{2} \pi r^2$
- $A = \frac{1}{2} \pi r$
- $A = \pi r^2$ (correct)
If a circle has a radius of 10 centimeters, what is its area?
If a circle has a radius of 10 centimeters, what is its area?
- $50\pi cm^2$
- $200\pi cm^2$
- $100\pi cm^2$ (correct)
- $25\pi cm^2$
If a circle has a diameter of 14 inches, what is its area?
If a circle has a diameter of 14 inches, what is its area?
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What does the number $\pi$ represent in the context of finding the area of a circle?
What does the number $\pi$ represent in the context of finding the area of a circle?
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Study Notes
Circumference and Diameter of a Circle
- The circumference of a circle is directly proportional to its diameter, with a constant of proportionality equal to π (pi)
- Circumference = π × diameter
Area of a Circle
- The formula for finding the area of a circle is: Area = π × radius²
- If the radius is not given, the formula can be rewritten as: Area = (π × diameter²) / 4
Calculating the Area of a Circle
- If the radius is 10 centimeters, the area of the circle is: π × 10² = approximately 314 square centimeters
- If the diameter is 14 inches, the area of the circle is: (π × 14²) / 4 = approximately 153.94 square inches
The Role of π in Finding the Area of a Circle
- π (pi) represents the ratio of a circle's circumference to its diameter, approximately equal to 3.14159
- π is used to calculate the area of a circle as it is a fundamental constant in circle geometry
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