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Year 8AC9M8M03

Circumference and Area of a Circle

Solve problems involving the circumference and area of a circle using formulas and appropriate units.

Two formulas, and one thing that decides which: does the question ask about the edge, or the inside?

Method

Circumference is the distance around
C=πd=2πrC = \pi d = 2\pi r
Use it for edges, rims, wheels and fences.
Area is the space inside
A=πr2A = \pi r^2
Use it for surfaces, lids and coverage.
Diameter is twice the radius
d=2rd = 2r
Halve the diameter before using the area formula.
Squaring only the radius
πr2 means π×r×r\pi r^2 \text{ means } \pi \times r \times r
Not $(\pi r)^2$. The $\pi$ is not squared.
Keep $\pi$ exact until the last line
Round once, at the end.

Worked example

e.g. A circle has diameter 10 cm. Find its circumference and area.\text{A circle has diameter } 10\text{ cm. Find its circumference and area.}
  1. Write down what you have.d=10∴r=5d = 10 \quad\therefore\quad r = 5
  2. For circumference, use the diameter form.C=πd=10πC = \pi d = 10\pi
  3. Round at the end.C≈31,4 cmC \approx 31{,}4 \text{ cm}
  4. For area, use the radius — halve the diameter first.r=5r = 5
  5. Substitute into the area formula.A=π(5)2=25πA = \pi(5)^2 = 25\pi
  6. Round, and use square units.A≈78,5 cm2A \approx 78{,}5 \text{ cm}^2

Practice

Ask first: edge or inside? Then check whether you were given rr or dd.

1
Find the circumference of a circle with r=7\text{Find the circumference of a circle with } r = 7
Answer14π≈44,014\pi \approx 44{,}0
2
Find the area of a circle with r=3\text{Find the area of a circle with } r = 3
Answer9π≈28,39\pi \approx 28{,}3
3
Find the area of a circle with d=8\text{Find the area of a circle with } d = 8
Answer16π≈50,316\pi \approx 50{,}3
4
A wheel has d=60 cm. How far in one turn?\text{A wheel has } d = 60\text{ cm. How far in one turn?}
Answer60π≈188,5 cm60\pi \approx 188{,}5 \text{ cm}
5
A circle has C=31,4. Find r.\text{A circle has } C = 31{,}4. \text{ Find } r.
Answerr=5r = 5
6
Why is πr2 not the same as (πr)2?\text{Why is } \pi r^2 \text{ not the same as } (\pi r)^2?
AnswerOnly the radius is squared.\text{Only the radius is squared.}
Next step
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