Question 35

The ratio of the area of a sector of a circle to the area of the circle is 1 : 4. If the area of the circle is 154 $$cm^{2}$$ , the perimeter of the sector is

Solution

area of the circle = $$ \pi r^2 = 154 $$

$$ \frac{22}{7} \times r^2 = 154 $$

on solving r =7

angle subtended by the sector at the centre = $$ 90^\circ $$

length of an arc = $$ \frac{\pi r \theta}{180} $$

= $$ \frac{22}{7} \times 7 \times \frac{90}{180} = 11 $$

perimeter of sector = $$ 2r + l = 2 \times 7 + 11 = 25 $$

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