If the area of a sector of a circle bounded by an arc of length 5$\pi$ cm is equal to 20$\pi$ cm2, then the radius of the circle

Question

KollegeApply · Accepted Answer

We have given length of the arc and area of the sector bounded by that arc and we are asked to find the radius of the circle. If l is the length of the arc, A is the area of the arc and r is the radius of the circle, then we know the expression of the area of the sector in terms of the length of the arc and radius of the circle. Area of the sector=$\frac{1}{2}$ lr Now we will substitute the corresponding values of length of the arc and area of the sector. $\therefore$ 20 pi=$\frac{1}{2}$xx5pixxr Multiplying both sides of the equation by 2 we get, 40pi=5pixxr Dividing both sides of the equation by 5piwe get, r=8 Therefore, radius of the circle is 8 cm

AChoose Your Answer