Page 76 - Mathematics Class - IX

3. 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 the base of cylinder, then circumference of the base of cylinder = 2pr

\ 2pr = a ...(i)

4. Height (h) of the cylinder = Breadth of rectangular paper = b

5. As on folding the rectangle, it becomes cylinder, so curved surface area of cylinder will be equal to the
area of rectangle.

\ Now, curved surface area of cylinder = Area of rectangle

= a × b = (2pr)h [from Eq. (i)]

= 2p rh sq units

OBSERVATIONS

By actual measurement,

a = ..............,

b = .................,

2pr = a = ..................,

h = b = ................,

Area of the paper = a × b = ....................

INFERENCE

Curved surface area of the cylinder = 2prh

EXTENDED TASK
1. Find the curved surface area of a cylindrical bucket in your home.

2. Make a cylindrical roller brush and observe how much area is covered in one revolution by painting a sheet.

APPLICATION

This activity can be used in finding the material used in making cylindrical containers, i.e. power tins, fuel drums,
oil tanks, jars used in industrial units, overhead water/fuel tanks, etc.

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