A circle has an area of 24 m^2. What is the area of a 45 degree sector of this circle?
Check the final answer first, then review the worked steps.
Problem
A circle has an area of 24 m^2. What is the area of a 45 degree sector of this circle?
Step-by-step solution
The area of a sector is proportional to the angle it subtends. The ratio of the sector's angle to the total angle in a circle (360 degrees) is $\frac{45^{\circ}}{360^{\circ}} = \frac{1}{8}$. Therefore, the area of the sector is $\frac{1}{8}$ of the total area of the circle: $\frac{1}{8} \times 24 \text{ m}^2 = 3 \text{ m}^2$.
Answer
$3 \text{ m}^2$