**NCERT Class 10 Maths Lab Manual – Area of Circle by Paper Cutting and Pasting Method**

**Objective**

To obtain the formula for area of the circle i.e., πr^{2} by paper cutting and pasting method.

**Prerequisite Knowledge**

**Definition of circle:**A circle is the locus of a point in a plane which moves in such a way that its distance from a fixed point remains constant. Fixed point is known as centre and the fixed distance is known as radius of the circle.

**Area of the circle:**It is the measure of the region of the plane enclosed by it.**Circumference of the circle:**Total length of its boundary.

(C = 2πr, where ris radius of the circle)

**Area of rectangle:**length x breadth.**Sectors of a circle.**

**Materials Required**

White paper, coloured sketch pen, a pair of scissors, fevicol, geometry box.

**Procedure**

- Draw a circle of any radius on a sheet of paper (Take r = 6.5 cm) using compass

- Fold it once along the diameter to obtain two semicircles as shown in fig. (ii).

- Again fold the semicircle to get quarters of circle.

- Repeat this process of folding upto four folds and then it looks like a small sector as shown in fig. (iv).

- Press and unfold the circle. It is divided into 16 equal sectors.

- Colour half of this circle i.e. 8 parts with one sectors with colour say blue and remaining 8 sectors different colour say orange.

- Cut these sixteen different sectors of circle.
- Cut one of the sector of orange colour into two equal parts as shown in the fig. (vii).

- Arrange these seventeen sectors (one orange sector is divided in two parts) in alternate manner so that they form a rectangular shape as shown in fig. (viii).

**Observation**

- Area of the rectangular shape so formed with seventeen sectors is same as the area of circle.
- Length of the rectangular shape = \(\frac { 1 }{ 2 }\) x circumference of circle = \(\frac { 1 }{ 2 }\) x 2πr = πr.
- Breadth of the rectangular shape = radius of circle

∴ Area of the rectangle = L x B = πr x r = πr^{2}sq. units.

**Result**

Area of a circle with radius r = πr^{2}.

**Learning Outcome**

- The figure formed by arranging 17 sectors of a circle is almost a rectangle.
- As we increase the number of sectors of the circle, the figure of rectangle becomes better and better.
- Through this activity, students will learn to find the approximate result for the area of a circle.

**Activity Time**

Find out the area of a circle of radius 6.3 cm by dividing the circle into 32 sectors.

You can also download **NCERT Solutions For Class 10** to help you to revise complete syllabus and score more marks in your examinations.

**Viva Voce**

**Question 1.**

Define concentric circles.

**Answer:**

Circles having same centre and different radii are called concentric circles.

**Question 2.**

Define sector

**Answer:**

It is the part of a circle between two radii and corresponding arc.

**Question 3.**

What shape will you obtain, if you rotate a circle along diameter ?

**Answer:**

Sphere

**Question 4.**

What is the area of a circular ring?

**Answer:**

π(R^{2} – r^{2}), where R = internal radius and r = internal radius of the ring.

**Multiple Choice Questions**

**Question 1.**

What is the radius of the circle if length of the arc is 22 cm and central angle is 30° ?

(a) 21cm

(b) 24 cm

(c) 42 cm

(d) None of these

**Question 2.**

Area of a quadrant of a circle in the form of its diameter d is

(a) \(\frac{\pi{d}^{2}}{8}\)

(b) \(\frac{\pi{d}^{2}}{16}\)

(c) \(\frac{\pi{d}^{2}}{4}\)

(d) None of these

**Question 3.**

If a chord subtends a right angle at the centre, then area of the corresponding segment

(a) \(\left(\frac{\pi}{4}-\frac{1}{2}\right)\) r^{2}

(b) \(\left(\frac{\pi}{4}+\frac{1}{2}\right)\)

(c) \(\left(\frac{1}{2}-\frac{\pi}{4}\right)\)

(d) None of these

**Question 4.**

Perimeter of sector of a circle of radius r is

(a) \(\frac{\pi r\theta}{{180}^{0}}\)

(b) \(\frac{\pi r\theta}{{180}^{0}}\) + 2r

(c) \(\frac{2\pi r\theta}{{360}^{0}}\) – 2r

(d) None of these

**Question 5.**

Angle described by hour hand in 12 hours is

(a) 180°

(b) 720°

(c) 360°

(d) None of these

**Answers**

- (c)
- (b)
- (a)
- (b)
- (c)

Math LabsScience LabsScience Practical SkillsMath Labs with Activity