Cogito
Grade 7 Math · Chapter 7 · Lesson 3
Area of a Circle
Why the radius is squared.
10 problems · about 19 minutes · 7.G.B.4
What this lesson teaches
The child finds the area of a circle from its radius or diameter.
- The area of a circle is πr².
- Halve a diameter before squaring, or the answer is four times too big.
- Doubling the radius quadruples the area.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Area of a Circle: Radius 4, π = 3.14. Area?
Answer 50.24
Why 50.24 cm².
Review — Measuring a Circle: Diameter 50, using π = 3.14. Circumference?
Answer 157
Why 157.
Review — Solving Inequalities: 4x > 20. Smallest whole number x?
Answer 6
Why 6.
Warm Up
Straightforward practice. Get the method working first.
3 problemsDiameter 16. What is r² ?
Answer 64
Why 64.
Radius 4. What is r² ?
Answer 16
Why 4 × 4.
Diameter 14. What is the radius?
Answer 7
Why Halve it.
Build It Up
The same ideas with more to keep track of.
2 problemsRadius 10. What is r² ?
Answer 100
Why 10 × 10.
Double the radius. How many times bigger is the area?
Answer 4
Why The radius is used twice.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Radius: Radius 3. What is r² ?
Answer 9
Why 9, so the area is 9π.
The Diameter: Diameter 12. What is r² ?
Answer 36
Why Radius 6, so 36.