Question

A sector of a circle with area $\frac{264}{7}	ext{ cm}^2$ is cut from a circle of radius $6	ext{ cm}$. The central angle of the sector is:

Accepted Answer

D. Area of sector $= \frac{	heta}{360^\circ} 	imes \pi r^2$ $$\frac{264}{7} = \frac{	heta}{360^\circ} 	imes \frac{22}{7} 	imes 6^2$$ $$\frac{264}{7} = \frac{	heta}{360^\circ} 	imes \frac{22 	imes 36}{7} \implies 264 = 	heta 	imes \frac{22}{10}$$ $$	heta = \frac{264 	imes 10}{22} = 120^\circ$$

Central angle of a sector

Explanation

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