124
Circle and cone
Textbook: Part 4, lesson 124, pp. 49–51
GoalCircle and cone: how a cone is formed; its base, apex and lateral surface; the volume of a cone and a cylinder.
New words
cone · konusapex of a cone · konus uchibase · asosleg · katet
Explanation
If a right triangle spins about one of its legs, it forms a cone. The leg on the axis becomes the height of the cone, and the other leg becomes the radius of the circular base. A cone has one circular base, one apex and a curved lateral surface. A cone with the same base and height as a cylinder has one third of the cylinder's volume.
Worked examples
A triangle with legs 3 cm and 4 cm spun about the 4 cm leg gives a cone of height 4 cm, base radius 3 cm and base diameter 6 cm.
If a cylinder has volume 90 cm³, the cone with the same base and height has volume 90 : 3 = 30 cm³.
Class activity
“Find the cone”: a bag holds a cone (ice-cream cone, paper hat), a cylinder and a sphere. A child feels one without looking and finds the cone by its apex and flat base.
Practice
1
A right triangle with legs 3 cm and 4 cm is spun about the 4 cm leg. What is the diameter in cm of the cone's base?
6
2
How many flat bases does a cone have?
1
3
Which of an ice-cream cone, a ball and a tin can is cone-shaped?
the ice-cream cone
4
A cylinder has volume 90 cm³. What is the volume in cm³ of a cone with the same base and height?
30
5
A cone has height 9 cm and base radius 4 cm. What is the base diameter in cm?
8