156
Circle and disc
Textbook: Part 4, lesson 146, pp. 64–65
GoalCircle and disc: how radius and diameter relate; expressions with letters; circle-drawing tasks.
New words
radius · radiusdiameter · diametrexpression with letters · harfli ifodaperimeter · perimetr
Explanation
Circles of the same size have equal diameters and equal radii. The radius is half the diameter: r = d : 2, and the diameter is twice the radius: d = r × 2. With letters: if the diameter is a cm, the radius is a : 2; a square with side k has perimeter k × 4; a rectangle with sides m and n has perimeter (m + n) × 2; a cuboid with dimensions f, g, h has volume f × g × h.
Worked examples
If d = 18 cm, then r = 18 : 2 = 9 cm.
A square with side 7 mm has perimeter 7 × 4 = 28 mm.
Class activity
“Chain of circles”: children draw several circles of radius 2 cm along a line: centres 3 cm apart, then 4 cm. They find the pattern and draw two more circles.
Practice
1
A circle has a diameter of 18 cm. What is its radius in centimetres?
9
2
A circle has a radius of 15 dm. What is its diameter in decimetres?
30
3
Write an expression for the radius of a circle with a diameter of a cm.
a : 2
4
A square has side 7 mm. What is its perimeter in millimetres?
28
5
x × 20 = 200, x = ?
10
6
800 : x = 10, x = ?
80
7
A road is 3 m wide. Can a disc with radius 2 m fit on it?
No: its diameter is 4 m, which is more than 3 m