Mathematics Lab Activity-18 Class X | Surface Area and Volume

By CBSE MATHEMATICS May 22, 2024

Mathematics Lab Activity-18 Class X

Mathematics Laboratory Activities on Surface Area and Volume for class X students with complete observation tables strictly according to the CBSE syllabus.

Chapter - 11

surface area and volume

Activity - 18

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, sketch pens, 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

$\Rightarrow 2\pi r=\frac{\theta}{360}\times 2\pi l$
$\Rightarrow r=\frac{\theta}{360}\times l$

8. Curved surface area of the cone

$=\large \pi rl$

$=\pi\times\left(\frac{\theta}{360}\times l\right)\times l$

$=\frac{\theta}{360}\times\pi l^{2}$

= Area of the sector.

So we have

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

Observations & calculations

On actual measurement :

1. For Circle

Let radius of circle = 7/2 cm.

Angle of sector = 90^o.

Length of arc $=\frac{\theta}{360}\times 2\pi l$ = 11/2 cm

Area of sector $=\frac{\theta}{360}\times\pi l^{2}$ = 77/8 cm².

2. For cone

Circumference of base of cone = Length of arc of circle

2πr = 11/2

r = 7/8 cm

Slant height of cone = Radius of circle = 7/ cm.

3. Curved surface area of cone

= πrl

= 77/2 cm².

Result

From the above observation we conclude that CSA of cone = Area of the sector of the circle from which the cone is formed.

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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