What is the area of a sector of a circle with a central angle of $90°$ and a radius of $1$ foot?

• A. $\pi$ square feet
• B. $\frac{1}{2}\pi$ square feet
• C. $\frac{1}{4}\pi$ square feet
• D. $\frac{1}{8}\pi$ square feet

Answer: (C)

Verified step by step guidance

1. Recall the formula for the area of a sector of a circle: \(\text{Area} = \pi r^{2} \times \frac{\theta}{360}\), where \(r\) is the radius and \(\theta\) is the central angle in degrees.
2. Identify the given values: the radius \(r = 1\) foot and the central angle \(\theta = 90^\circ\).
3. Substitute the given values into the formula: \(\text{Area} = \pi \times 1^{2} \times \frac{90}{360}\).
4. Simplify the fraction \(\frac{90}{360}\) to its lowest terms to make the calculation easier.
5. Multiply \(\pi\), the radius squared, and the simplified fraction to express the area of the sector in terms of \(\pi\).