Question

question 1
if the area of the circle below is 10 in², what is the area of the shaded sector?
image of a circle with a 90° shaded sector
○ 5 in²
○ 2.5 in²
○ 3 in²
○ 7.5 in²

Explanation:

Step1: Determine the fraction of the circle the sector represents

The central angle of the shaded sector is \(90^\circ\), and a full circle is \(360^\circ\). So the fraction of the circle the sector is, is \(\frac{90}{360}=\frac{1}{4}\).

Step2: Calculate the area of the shaded sector

The area of the circle is \(10\space \text{in}^2\). The area of the sector is the fraction of the circle times the area of the circle. So, \(10\times\frac{1}{4} = 2.5\space \text{in}^2\).

Answer:

2.5 in² (corresponding to the option with 2.5 in²)