123
A cylinder and its net
Textbook: Part 4, lesson 123, pp. 46–48
GoalThe net of a cylinder: two circles and a rectangle; how the rectangle's sides relate to the cylinder's dimensions.
New words
net · yoyilmacircumference (length of circle) · aylana uzunligiwrapping · o‘rashlateral surface · yon sirt
Explanation
The net of a cylinder: the lateral surface is a rectangle and the two bases are equal circles. One side of the rectangle equals the height of the cylinder and the other equals the length of the base circle. We can measure the circle's length with a thread: wrap it around the circle, then stretch it and measure with a ruler. Lateral surface area = circle length × height.
Worked examples
Circle length 31 cm and height 10 cm: lateral surface 31 × 10 = 310 cm².
A can label: circle length 20 cm, height 8 cm: paper area 20 × 8 = 160 cm².
Class activity
“Measure with a thread”: children measure the circle around a glass or can with a thread and draw the rectangle of its lateral net in their notebooks.
Practice
1
How many pieces make the net of a cylinder?
3
2
The lateral net of a cylinder is a 31 cm × 10 cm rectangle. What is its area in cm²?
310
3
A cylinder has height 12 cm and base circle length 25 cm. What is the perimeter in cm of the rectangle of its lateral net?
74
4
A can label is 20 cm long (around the can) and 8 cm high. What is the area of the label in cm²?
160
5
A thread wrapped around the base of a cylinder measures 24 cm. How many cm is the matching side of the rectangle in the net?
24