121
Circle and sphere
Textbook: Part 4, lesson 121, pp. 40–42
GoalCircle and sphere: centre, radius, diameter, circumference; how a sphere is formed.
New words
circle (disc) · doiracircle line (circumference) · aylanaradius · radiusdiameter · diametr
Explanation
The boundary of a circle (disc) is the circle line. A segment from the centre to any point on the circle line is a radius; a segment joining two points on the circle line and passing through the centre is a diameter. Diameter = 2 × radius. If a disc spins about its diameter, it forms a sphere. A sphere has no faces, edges or vertices. Cutting a sphere through its centre gives a disc.
Worked examples
If the radius is 7 cm, the diameter is 7 × 2 = 14 cm. If the diameter is 18 cm, the radius is 18 : 2 = 9 cm.
The Earth's radius is about 6 400 km, so its diameter is about 12 800 km.
Class activity
“With a compass”: children draw a circle with a compass, mark the centre, draw a radius and a diameter, and measure to check the diameter is twice the radius.
Practice
1
How many centimetres is the diameter of a circle with radius 7 cm?
14
2
How many centimetres is the radius of a circle with diameter 18 cm?
9
3
The distance from the centre of a sphere to its surface is 5 cm. What is the diameter in cm of the largest circle you can cut from it?
10
4
4 identical circles, each of diameter 6 cm, touch in a row. How many cm long is the row?
24
5
The Earth's radius is about 6 400 km. About how many km is its diameter?
12800