92
Dividing a circle into equal parts
Textbook: Part 3, lesson 92, pp. 72–74
GoalDividing a disc into equal parts, called sectors, with radii and diameters.
New words
sector · sektorequal parts · teng bo‘laklarfolding · buklashstained glass · vitraj
Explanation
A disc can be divided into parts by radii drawn from the centre. Each such part is called a sector. One diameter divides a disc into 2 equal sectors. A horizontal and a vertical diameter give 4 equal sectors with right angles. Folding a disc in half twice also gives 4 equal parts. The number of radii equals the number of sectors.
Worked examples
A pizza is cut into 8 equal pieces: 8 sectors, 8 radii.
Two diameters (horizontal and vertical) give 4 sectors, and three diameters give 6 sectors.
Class activity
“Folding the disc”: a paper disc is folded twice to make 4 sectors; one more fold makes 8; the parts are counted each time.
Practice
1
3 diameters were drawn in a disc. How many sectors were formed?
6
2
If 6 radii are drawn from the centre of a disc at equal angles, how many equal sectors are formed?
6
3
A stained-glass picture has coloured and clear pieces; there are 3 times as many clear pieces as coloured ones. If there are 80 pieces in total, how many are clear?
60
4
A stained-glass picture has a rectangular piece 90 cm × 60 cm and two round pieces, each with an area half that of the rectangle. What is the total area in cm²?
10800
5
A pie of 1 kg 200 g was cut into 12 equal pieces. 5 pieces were eaten. How many grams are left?
700