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# Maths Art Integrated Activity 2022-23.pptx

Maths Art Integrated Activity 2022-23.pptx

Maths Art Integrated Activity 2022-23.pptx

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### Maths Art Integrated Activity 2022-23.pptx

1. 1. Mathematics Art Integrated Activity
2. 2. JAWAHAR NAVODAYA VIDYALAYA KHEDGAON, NASHIK 2022-23 Name- Swadesh Shivaji Jadhav Class – 10 Div - 'A' Roll no. - 1035/35 Sub - Mathematics Guided By- A. D. Shinde sir
3. 3. contents Circle and its related terms . Area of a circle . Perimeter of a circle Sector of a circle and its area . Segment of a circle and its area Areas of combinations of plane figures
4. 4. • Circle and its related terms Circle – Definition The collection of all the points in a plane which are at a fixed distance from in the plane is called a circle . Or A circle is a locus of a point which moves in a plane in such a way that its distance from a fixed point always remains same.
5. 5. Terms Related to Circles
6. 6. 1. Radius – The line segment joining the centre and any point on the circle is called a radius of the circle .
7. 7. 2. A circle divides the plane on which it lies into three parts . They are • The Interior of the circle . • The circle . Exterior • The exterior of the circle . Here , in the given fig. We can see that point B is in the cricle, point A is on the circle and point A is in exterior of the circle
8. 8. 3. Chord – if you take two points P and Q on a circle , then the line segment PQ is called a chord of the circle 4. Diameter – the chord which passes through the centre of the circle is called a diameter of the circle Here in the given fig. OR is the diameter of the circle and PR is the chord of the circle . Note :- A diameter of a circle is the longest chord of the circle
9. 9. • Arc, Segment and Sector of a Circle 1. Arc of a Circle The arc of a circle is defined as the part or segment of the circumference of a circle. If the length of an arc is exactly half of the circle, it is known as a semicircular arc. Here in the given fig. ACB is the major arc because it is the longer one whereas AB is the minor arc of the given circle.
10. 10. 2.Segment - the region between a chord and either of its arc is called a segment of the circle.
11. 11. 3. Sector - the region between two radii, joining the centre to the end points of the arc is called a sector Here in the given fig. you find that minor arc corresponds to minor sector and major arc corresponds to major sector.
12. 12. • Circumference of a Circle The perimeter of a circle is its boundary or the complete arc length of the periphery of a circle. We know that circumference of a circle bears a constant ratio with its diameter . Circumference = 2𝜋r
13. 13. • Area of a Circle Area of a circle is 𝜋rxr, where r is the radius of the circle. We have verified it in class 7, by cutting a circle into a number of sectors and rearranging them as shown in fig.
14. 14. • Area and circumference of semicircle
15. 15. • Area of a Sector • Following are some important points to remember • 1.A minor sector has an angle 𝜃, (say), subtended at the centre of the circle , whereas a major sector has no angle . • 2.The sum of arcs of major and minor sectors of a circle is equal to the circumference of the circle. • 3.The sum of the areas of major and minor sectors of a circle is equal to the areas of the circle. • 4.The boundary of a sector consists of an arc of the circle and the two radii.
16. 16. • Area of a Sector
17. 17. Area of a segment of a circle