Cogito
Integrated Math 2 · Chapter 6 · Lesson 1
Circumference, Area, and Arcs
Measuring a circle and a piece of one.
12 problems · about 21 minutes · G-C.B.5, G-GMD.A.1
What this lesson teaches
The student computes circumference, area, arc length and sector area.
- Circumference is 2πr and area is πr².
- An arc or sector is the fraction angle ÷ 360 of the whole.
- Both formulas use the radius, never the diameter.
Warm Up
Straightforward practice. Get the method working first.
5 problemsRadius 7. What is the area divided by π?
Answer 49
Why 49.
How can you tell which formula gives area?
Answer Area is in square units, so it uses a squared length.
Why The squared radius gives square units.
Radius 5. Circumference divided by π?
Answer 10
Why 2 × 5.
Radius 5. Area divided by π?
Answer 25
Why 5².
Diameter 12. What is the radius?
Answer 6
Why Half.
Build It Up
The same ideas with more to keep track of.
3 problemsA 90° sector is what fraction of the circle, as a decimal?
Answer 0.25
Why 90 ÷ 360.
A 120° sector is what fraction, to three decimal places?
Answer 0.333
Why 120 ÷ 360.
Radius 6, 180° sector. Arc length divided by π?
Answer 6
Why Half of 12π.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each formula by what it measures.
Answer Measures a length: Two pi r, Arc length · Measures an area: Pi r squared, Sector area
Why Anything squared measures an area.
Radius 3. Area divided by π?
Answer 9
Why 3².
The Circumference: A circle has radius 10. What is the circumference divided by π?
Answer 20
Why 20, so the circumference is 20π.
The Area: Same circle. What is the area divided by π?
Answer 100
Why 100, so the area is 100π.