Question

# In a circle of radius $$\displaystyle 10.5 \ cm$$, the minor arc is one-fifth of the major arc. Find the area of the sector corresponding to the major arc.

Solution

## Radius of circle =$$\displaystyle 10.5 \ cm$$Let $$\displaystyle x \ cm$$ be the major arc, then $$\displaystyle \dfrac{x}{5} \ cm$$ be the length of minor arc.Circumference of circle = $$\displaystyle x + \dfrac{x}{5} = \frac{6x}{5}$$We know, Circumference of circle = $$\displaystyle 2\pi r = 2 \times \frac{22}{7} \times 10.5$$ This implies,$$\displaystyle \frac{6x}{5} = 2 \times \frac{22}{7} \times 10.5$$$$\displaystyle x = 55 \ cm$$Area of major sector $$=\dfrac{\text{length of arc}}{2\pi r}\times\pi r^2=\displaystyle \frac{1}{2} \times 55 \times 10.5 = 288.75$$The area of major sector is $$\displaystyle 288.75 \ cm^2$$.MathematicsRS AgarwalStandard X

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