1. **Stating the problem:** Find the area of circular sectors with given radii and angles. 2. **Formula for the area of a circular sector:** The area $A$ of a sector with radius $r$ and central angle $\theta$ (in radians) is given by: $$A = \frac{1}{2} r^2 \theta$$ 3. **Important notes:** - The angle must be in radians. - If the angle is given in terms of $\pi$, use it directly. 4. **Problem a:** radius $6$ cm, angle $c$ (assuming $c$ is in radians) $$A_a = \frac{1}{2} \times 6^2 \times c = 18c$$ 5. **Problem b:** radius $10$ cm, angle $\frac{7\pi}{10}$ $$A_b = \frac{1}{2} \times 10^2 \times \frac{7\pi}{10} = \frac{1}{2} \times 100 \times \frac{7\pi}{10} = 50 \times \frac{7\pi}{10} = 35\pi$$ 6. **Problem c:** radius $15$ cm, angle $53$ (assuming degrees, convert to radians) Convert $53^\circ$ to radians: $$53^\circ = 53 \times \frac{\pi}{180} = \frac{53\pi}{180}$$ Area: $$A_c = \frac{1}{2} \times 15^2 \times \frac{53\pi}{180} = \frac{1}{2} \times 225 \times \frac{53\pi}{180} = 112.5 \times \frac{53\pi}{180} = \frac{5962.5\pi}{180} = \frac{11925\pi}{360}$$ 7. **Problem d:** radius $9$ cm, angle $s$ (assuming $s$ in radians) $$A_d = \frac{1}{2} \times 9^2 \times s = \frac{1}{2} \times 81 \times s = 40.5s$$ **Final answers:** - a) $18c$ cm$^2$ - b) $35\pi$ cm$^2$ - c) $\frac{11925\pi}{360}$ cm$^2$ - d) $40.5s$ cm$^2$