Circles

Measure around any circle and divide by the distance across. You always get the same number, $π \approx 3.14$ . So $C = π d = 2 π r$ .

The radius

r

goes from the center to the edge. The diameter is twice that.

For area, cut a circle into thin slices and line them up alternating. It looks like a rectangle $π r$ long and $r$ tall, which gives $A = π r^{2}$ .

Circumference is a length, so

r

appears once. Area is square units, so

r

is squared.

Work through it

Convert to the radius. $r = 5$

Square, then multiply by $π$ . $A = 25 π \approx 78.5$

Find $r$ first. $r^{2} = 49$ , so $r = 7$

Use the other formula. $C = 14 π$

The slice is $\frac{1}{4}$ of the circle. $\frac{1}{4} π (8)^{2}$

Simplify. $16 π$

Using the diameter in $π r^{2}$ .

Halve it first. With diameter 10, the area is $25 π$ , not $100 π$ .

The short version
Circumference is

2 π r

, and area is

π r^{2}

. Check whether you were given the radius or the diameter.

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