Mathematics Lab Activity-14 Class IX | Surface Area & Volume

 Lab Activity-14 Class iX

Mathematics Lab Activities on Surface area and volume for class IX students, with complete observation tables, strictly according to the CBSE syllabus.

Chapter - 11  surface area & volume

Activity - 14

Objective: 

To form a cone from a sector of a circle and to find the formula for its curved surface area.

Material Required:

Wooden hardboard, acrylic sheets, cellotape, glazed papers, sketchpens, white paper, nails, marker.

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 [see Fig. 1].

Figure 1

3. Cut out a sector of angle q degrees from the circle [see Fig. 2].

Figure 2

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 [see Fig. 3].

Figure 3

5. Slant height of the cone = radius of the circle = l.

6. Radius of the base of the cone = r.

7. Circumference of the base of the cone = Arc length of the sector = 2πr.

8. Curved surface area of the cone = Area of the sector.

 

Observations
On actual measurement :

The slant height l of the cone = 25 cm, r =7 cm.

So, arc length of circle = Circumference of base of cone = 2πr = 44 cm,

Area of the sector = 550 cm².

Curved surface area of the cone = 550 cm².

Therefore, curved surface area of the cone = Area of the sector = 550 cm².

Result : 

With this activity we drive the formula for finding the curved surface area of cone which is equal to πrl.

Applications

The result is useful in

1. Estimating canvas required to make a conical tent

2. Estimating material required to make Joker’s cap, ice cream cone, etc.

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