Two circular sectors, Sector P and Sector Q

MATHEMATICS · Multi-part · CBSE · Mathematics · Areas Related to Circles · Areas Related to Circles

Problem

Two circular sectors, Sector P and Sector Q, have equal areas. Sector P has radius 8 cm and central angle θ1\theta_1, while Sector Q has radius 6 cm and central angle θ2\theta_2. (Use π=227\pi = \dfrac{22}{7} in numerical calculations.) (i) Derive, in simplest form, the relation between θ1\theta_1 and θ2\theta_2. (ii) If θ1=120∘\theta_1 = 120^\circ, calculate the value of θ2\theta_2. (iii) For Sector P with θ1=120∘\theta_1 = 120^\circ, find the length of its arc.

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