Areas Related to Circles

This chapter measures the parts of a circle. Starting from the circumference $2\pi r$ and area $\pi r^2$ of a circle and the area of a ring, it develops the two central formulae — the area of a sector $\frac{\theta}{360}\pi r^2$ and the length of an arc $\frac{\theta}{360}\times 2\pi r$ — and then the area of a segment as (area of sector $-$ area of triangle). These are applied to a wide range of board favourites: minute and hour hands of clocks, windscreen wipers, grazing animals tied by a rope, umbrellas and fans, and especially areas of combinations of plane figures (shaded regions built from circles, sectors, squares and triangles). It is a formula-rich, high-scoring chapter of the Class 10 Board syllabus.