89
Circles and their boundary
Textbook: Part 3, lesson 89, pp. 64–66
GoalCircle (outline) and disc; centre, radius, diameter; the diameter is twice the radius.
New words
circle (the curve) · aylanadisc (the filled circle) · doiraradius · radiusdiameter · diametr
Explanation
A circle is the closed line of all points at the same distance from one point, the centre. A disc is the circle together with its inside; the circle is the boundary of the disc. A segment joining the centre to a point on the circle is a radius. A segment through the centre joining two points of the circle is a diameter. Any number of radii and diameters can be drawn; they are all equal: diameter = radius × 2.
Worked examples
If the radius is 5 cm, the diameter is 5 × 2 = 10 cm.
If the diameter is 3 m 8 dm = 38 dm, the radius is 38 : 2 = 19 dm = 1 m 9 dm.
Class activity
“Where is the circle?”: children find round objects in class (clock, coin, plate), tell the circle from the disc and measure the diameter with a ruler.
Practice
1
A circle has radius 7 cm. How many centimetres is its diameter?
14
2
A circle has diameter 18 cm. How many centimetres is its radius?
9
3
A round playground has diameter 6 m 40 cm. How many centimetres is its radius?
320
4
A path is laid along the diameter of a round flowerbed with radius 3 m. How many metres long is the path?
6
5
Two circles have radii 5 cm and 8 cm. By how many centimetres do their diameters differ?
6