Question

Find the measure of the central angle with a radius of 18 inches and the area of a sector measuring 40.5π square inches.

Answer 1

$\text{Area of sector}= \cfrac{\theta \pi r^2}{360^o} \ \ \ \ \ \text{[when r is a radius, } \theta \text{ is the central angle]} \\ \\ 40.5 \pi = \cfrac{\theta* \pi* 18^2}{360^o} \ \to \ 14580 \pi = \theta* \pi* 324 \ \to \ \\ \\ \theta= \cfrac{14580 \pi }{324 \pi }= 45^o$