Page 73 - Mathematics Class - IX

PROCEDURE
1. Take a wooden hardboard of a convenient size and paste a white paper on it.
2. Cut out a circle of radius l from a acrylic sheet (Fig. (c)).

3. Cut out a sector of angle q degrees from the circle (Fig. (d)).

Fig. (c) Fig. (d)

4. Bring together both the radii of the sector to form a cone and paste the ends using a
cellotape and fix it on the hardboard (Fig. (e)).
5. Radius of the base of the cone = r
6. Slant height of the cone = Radius of the circle = l

7. Circumference of the base of the cone = Arc length of the sector = 2pr Fig. (e)
8. Now, curved surface area of the cone = Area of the sector
Arclength
= × Area of the circle
Circumferenceofcircle
2πr
2
= 2πl × πl = πrl

OBSERVATIONS
By actual measurement,
The slant height (l) of the cone = ................., and radius (r) = .................
\ Arc length (2pr) = .................

Area of the sector = ................., curved surface area of the cone = .................
Hence, curved surface area of the cone = Area of the sector.

INFERENCE

The formula for calculating the curved surface area of a cone is prl.

EXTENDED TASK
1. Calculate the curved surface area of a birthday cap.
2. After forming a cone from the sector of a circle, verify experimentally that curved surface area of cone is
equal to the area of the sector.

APPLICATION
The result is useful in estimating canvas required to make a conical tent and to estimate material required to make
joker’s cap, ice-cream cone, etc.

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