Question

A sector has area of 314.16 cm² and a central angle of 90°. What is its radius?

• A. 20
• B. 20.14
• C. 20.28
• D. 20.42

Answer 1

Answer:

A. 20

The correct answer is Option A (20 cm).

To find the radius, we use the formula for the area of a sector, which represents a "slice" of a full circle.

Step-by-Step Solution

1. Use the Sector Area Formula:
   $\text{Area} = \frac{\theta}{360} \times \pi r^2$

   • Where $\theta$ is the central angle ($90^\circ$).

   • $\text{Area} = 314.16 \text{ cm}^2$.

2. Substitute the Given Values:
   $314.16 = \frac{90}{360} \times \pi r^2$

3. Simplify the fraction: $90/360 = 1/4$.
   $314.16 = \frac{1}{4} \times \pi r^2$

4. Solve for $r^2$:
   Multiply both sides by 4:
   $1256.64 = \pi r^2$
   $r^2 = \frac{1256.64}{3.1416} = 400$

5. Find the Radius:
   $r = \sqrt{400} = \mathbf{20 \text{ cm}}$