Areas Related To Circles Class 10 Notes Maths: Chapter 12

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    Basic Concepts-01
    Chap 12-01
    • Distance moved by a wheel in 1 rotation = Circumference of the wheel.
    • Number of rotation by a wheel in 1 minute = Distance moved by wheel in 1 minute / Circumference of wheel.
    • For a circle having radius r.
      (i) Diameter = 2r
      (ii) Circumference = 2πr
      (iii) Area = πr2 
      (iv) Area of semi-circle =r2/2
      (v) Area of a quadrant =r2/4
      (vi) Perimeter of semi-circle = (πr + 2r)
    • If R and r are the radii of two concentric circles such that R > r then,The area enclosed between the two circles = πR2 – πr2 = π(R2 – r2)
    • A segment of a circle is the region bounded by a chord and the arc subtended by the chord

    $$If \space a \space sector\space of \space a \space circle \space of \space radius\space r\space contains\space an\space angle\space of\space \theta°, then$$

    $$\\(i)\space Length\space of\space the\space arc\space of\space the\space sector =\frac{\theta}{{360°}}×2\pi r=\frac{\theta}{{360°}}×(Circumference\space of\space the\space circle)$$

    $$\\(ii) Perimeter\space of\space the\space sector\space = 2r+\frac{\theta}{{360°}}×2\pi r$$

    $$\\ (iii) Area\space of\space the\space sector\space = \frac{\theta}{{360°}}×\pi r^2=\frac{\theta}{{360°}}×(Area of the circle)$$

    $$\\ (iv) Area\space of\space the\space minor\space segment = Area\space of\space the\space corresponding\space sector – Area\space of\space the\space corresponding\space triangle$$

    $$\\ =\frac{\theta}{{360°}}×\pi r^2– r^2 \space sin\space\frac{\theta}{{2}}cos\space\frac{\theta}{{2}}$$

    $$\\ =\set{\frac{\theta}{{360°}}×\pi – \space sin\space\frac{\theta}{{2}}cos\space\frac{\theta}{{2}}}r^2$$

    $$\\ =\set{\frac{\theta}{{360°}}×\pi – \space \space\frac{1}{{2}}sin\space{\theta}{}}r^2$$

    $$\\(iv) Area\space of\space the\space major\space segment\space = Area\space of\space the\space circle\space – Area\space of\space the\space minor\space segment$$