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

1. Coloured chart paper
2. Adhesive tape
3. Ruler
4. Pencil
5. Scissors

Prerequisite Knowledge

1. Concept of a rectangle and its area.
2. Concept of circle and terms related to it.
3. Concept of a cylinder.

Theory

1. For concept of rectangle and its area refer to Activity 3.
2. For concept of circle and related terms refer to Activity 23.
3. 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, the line AB is the generating line and PQ joining the centres of the circular base and top is called the axis. Also, circle BC is the base pf the cylinder.

Procedure

1. Take a rectangular chart paper having length a units and breadth b units, (see Fig. 29.3)
   
2. Now, folding the chart paper along its breadth, fix both ends by using adhesive tape and obtain a cylinder. (see Fig. 29.4)
   

Demonstration

1. 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)
2. Height (h) of the cylinder = Breadth of rectangular paper = b
3. 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.