About Lesson
Math Lab Activity
– Find a Formula for the Curved Surface Area of a Cylinder
Objective:
To find a formula for the curved surface area of a right circular cylinder, experimentally.
Materials Required:
- Coloured chart paper
- Adhesive tape
- Ruler
- Pencil
- Scissors
Prerequisite Knowledge:
- Concept of a rectangle and its area.
- Concept of circle and terms related to it.
- Concept of a cylinder.
Theory:
- For the concept of the rectangle and its area refer to Activity 3.
- For the concept of circle and related terms refer to Activity 23.
- A solid generated by the revolution of a rectangle about one of its sides which is kept fixed is called a right circular cylinder. The fixed side of the rectangle about which it rotates, is called the axis of the cylinder, (see Fig. 29.1)
In Fig 29.2, line AB when moving on the circumference of the circle BC generates a right circular cylinder. Here, line AB is the generating line and PQ joining the centers of the circular base and top is called the axis. Also, circle BC is the base of the cylinder.
Procedure:
- Take a rectangular chart paper having length a units and breadth b units, (see Fig. 29.3)
- Now, folding the chart paper along its breadth, fix both ends by using adhesive tape and obtain a cylinder. (see Fig. 29.4)
Demonstration:
- On folding the rectangle, the length of rectangle becomes circular base of the cylinder.
i.e. Circumference of the base of cylinder = Length of rectangular paper = a.
Let r be the radius of base of cylinder, then circumference of the base of cylinder = 2πr
2πr = a ………(i) - Height (h) of the cylinder = Breadth of rectangular paper = b
- As on folding the rectangle, it becomes cylinder, so curved surface area of cylinder will be equal to area of rectangle.
Now, curved surface area of cylinder = Area of rectangle
= a x b = (2πr)h [from Eq. (i)]
= 2πrh sq units
Observation:
By actual measurement,
a = ……..
b = ……….
2πr = a = ……….
h = b = ………….
Area of the paper = a x b = ………….
Hence, curved surface area of the cylinder = 2πrh
Result:
We have got the formula for curved surface area of a right circular cylinder, experimentally.
Application:
This activity can be used in finding the material used in making cylindrical containers, i.e. powder tins, fuel drums, oil tanks, jars used in industrial units, overhead water/fuel tanks, etc.
This activity can be used in finding the material used in making cylindrical containers, i.e. powder tins, fuel drums, oil tanks, jars used in industrial units, overhead water/fuel tanks, etc.