125
A cone and its net
Textbook: Part 4, lesson 125, pp. 52–54
GoalThe net of a cone: a circle and a sector; the arc of the sector equals the base circle.
New words
sector · sektorarc · yoynet of a cone · konus yoyilmasilength of the circle · aylana uzunligi
Explanation
The net of a cone has two parts: the base, a circle, and the lateral surface, a sector (a part of a circle). The length of the sector's arc equals the length of the base circle of the cone. If a circle is split into several equal sectors, their areas are equal; a sector is written as a fraction of the whole circle: 3 of 8 equal sectors is 3/8.
Worked examples
A circle of area 120 cm² is split into 8 equal sectors: one sector is 120 : 8 = 15 cm².
If the cone's base circle is 20 cm, the arc of the sector in the net is also 20 cm.
Class activity
“Paper hat”: children cut a sector out of a paper circle (with an adult's help), roll it into a cone hat and see how the arc becomes the circle at the base.
Practice
1
How many pieces make the net of a cone?
2
2
A circle is split into 8 equal sectors. What part of the circle is 3 sectors?
3/8
3
A circle of area 120 cm² is split into 8 equal sectors. What is the area of one sector in cm²?
15
4
The base circle of a cone is 20 cm long. How many cm is the arc of the sector in its net?
20
5
How many pieces (circles and sectors) are there in the nets of 6 such cones?
12