The area of a sector of a circle is 308 cm², with the central angle measuring 45°. What is the radius of the circle?

Question: The area of a sector of a circle is 308 cm², with the central angle measuring 45°. What is the radius of the circle?

Answer: 

28 cm

Additional Information :

We use the formula for the area of a sector of a circle:

$$A = \frac{\theta}{360^\circ} \times \pi r^2$$

where:

• $A = 308$ cm² (given area)
• $\theta = 45^\circ$ (central angle)
• $r$ = radius (to be found)
• $\pi \approx 3.1416$

Substitute the given values

$$308=\frac{45}{360}\times \pi r^2$$

Since $\frac{45}{360}=\frac{1}{8}$, we rewrite the equation as:

$$308=\frac{1}{8}\times \pi r^2$$$$r^2=\frac{308\times 8}{\pi }$$$$r^2=\frac{2464}{3.1416}$$$$r^2\approx 785$$

$$r\approx \sqrt{785}$$$$r\approx 28\text{ cm}$$

The radius of the circle is 28 cm.

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