Circumference and Area of a Circle and a Sector
Circumference of a circle is the distance around its edge, found with C = 2πr, where r is the radius. A circle with radius 5 has C = 10π. The area of a circle is the space inside it, found with A = πr².
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π and Circumference
- is a number used in circle formulas and is usually rounded to 3.14 in calculations.
- The formula for circumference is or .
Finding the Circumference of a Circle
- If the radius is , substitute into .
- This gives , which is approximately .
Finding the Area of a Circle
- The formula for circle area is .
- If the radius is , the area is , about .
Circle Sectors
- A sector is a fraction of a circle based on the central angle.
- Use for arc length and for area.
Practice Questions
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A circle has a radius of . What is the circumference of the circle?
Correct! 🎉 +10 pointsNot quite right
The formula for the circumference of a circle is . Since the radius is , the circumference is .
A circle has a diameter of . What is the circumference of the circle?
Correct! 🎉 +10 pointsNot quite right
The formula for the circumference of a circle is . Since the diameter is , substituting into the formula gives .
The radius of a circle is . What is the area of the circle in terms of ?
Correct! 🎉 +20 pointsNot quite right
The formula for the area of a circle is . Since the radius is , the area is .
The diameter of a circle is . What is the area of the circle in terms of ?
Correct! 🎉 +20 pointsNot quite right
The formula for the area of a circle is . Since the diameter is , the radius is cm. Substituting into the formula gives .
A sector of a circle has a central angle of and a radius of . What is the area of the sector in terms of ?
Correct! 🎉 +20 pointsNot quite right
The formula for the area of a sector is , where is the central angle. Here, and cm. So, cm².
A sector of a circle has a central angle of and a radius of . What is the arc length of the sector in terms of ?
Correct! 🎉 +30 pointsNot quite right
The formula for the arc length of a sector is , where is the central angle. Here, and cm. So, cm.
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Students Also Ask
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The circumference of a circle uses two forms of the same formula. With the diameter, C = πd. With the radius, C = 2πr, because the diameter is twice the radius. Both give the distance around the circle, roughly 3.14 times the diameter.
No, 3.14 is only an approximation of pi. Pi is a mathematical constant with infinite decimal places and no repeating pattern, so its digits never stop. We use 3.14 as a convenient rounded value, but the true value of π carries on forever.
The area of a circle is A = πr², where r is the radius. Square the radius first, then multiply by π. For example, a circle with radius 3 cm has an area of 9π cm². That is about 28.26 cm².
The main link between them is size. In any circle, the diameter is exactly twice the radius (d = 2r). So the diameter is always the longer measurement. If you know one, you can find the other: double the radius, or halve the diameter.
Because a sector is simply a fraction of the whole circle. You find that fraction from its central angle over 360. Then you take the same fraction of the full circle's circumference and area. So no separate sector formulas are needed.
A sector's fraction comes from its central angle. Divide the central angle by 360 to get the fraction of the whole circle. For example, a central angle of 60° gives 60/360. That simplifies to 1/6, so the sector is one sixth of the circle.