Study Notes
In this topic, you will learn how to calculate the area and circumference of circles, as well as the perimeter and area of circular sectors.
- Circle — a plain figure enclosed by a curved line, every point on which is equidistant from a point within, called the center. Example: A round plate is a circle.
- Radius — the distance from the center to the curve of the circle. Example: If a circle's radius is 5 cm, the distance from the center to any point on the circle is 5 cm.
- Circumference — the boundary of a circle. Example: The circumference of a circle with radius 3 cm is 6π cm.
- Diameter — any straight line passing through the center and touching the circumference at each end, equal to 2 times the radius. Example: If the radius is 4 cm, the diameter is 8 cm.
- Sector — the region contained between two radii of a circle. Example: A slice of pizza is a sector of a circle.
Exam Tips
Key Definitions to Remember
- A circle is a plain figure with all points equidistant from the center.
- The radius is the distance from the center to the circumference.
- The circumference is the perimeter of the circle.
- The diameter is twice the radius.
- A sector is a portion of a circle defined by two radii.
Common Confusions
- Confusing the radius with the diameter.
- Forgetting that the circumference is the perimeter of the circle.
Typical Exam Questions
- What is the area of a circle with radius 6 cm? Answer: 36π cm²
- Calculate the circumference of a circle with diameter 10 cm. Answer: 10π cm
- Find the perimeter of a sector with radius 5 cm and angle 90°. Answer: (5π/2 + 10) cm
What Examiners Usually Test
- Understanding and applying the formulas for area and circumference.
- Calculating the perimeter and area of sectors.
- Distinguishing between radius, diameter, and circumference.