44
Area of a circle
Textbook: pp. 120–121
GoalKnow the notions of a disc, its centre and radius; apply the disc area formula S = πR²; tell a circle from a disc.
New words
disc (circular region) · doiraarea of a disc · doira yuziS = πR² · S = πR²annulus (ring) · halqa
Explanation
A circle is a curve, while a disc is the circle together with all the points inside it: the points at distance at most R from the centre. The area of a disc is S = πR²; we get it because the areas of regular n-gons inscribed in and circumscribed about the circle approach πR² as n grows. If the diameter d is given, S = πd²/4. Doubling the radius makes the area four times larger, since the area is proportional to the square of the radius. The annulus between two concentric circles has area S = π(R² − r²).
Worked examples
R = 5: S = π·25 = 25π.
An annulus with outer radius 7 and inner radius 4: S = π(49 − 16) = 33π.
Class activity
“Paper disc”: with an adult's help cut a disc into 16 equal pieces and lay them alternately to form a near-rectangle; its length is about πR and its width R.
Practice
1
What is the area of a disc of radius 10 cm?
100π
2
What is the area of a disc with diameter 8 m?
16π
3
A disc has area 49π. What is its radius?
7
4
Why does the area become 9 times larger when the radius becomes 3 times larger?
The area is proportional to R², and (3R)² = 9R².