A circle has a radius of 5 units. What is the area of a sector with a central angle of 120 degrees?

Mon, 04 May 2026 00:32:19 +0000

**The Science Behind Circular Sectors: Area of a 120-Degree Slice** Curious about how circles shape everyday calculations? A simple yet vital query often surfaces online: *What is the area of a sector in a circle with a 5-unit radius and a 120-degree central angle?* This question isn’t just academic—it reflects growing interest in geometry’s role in design, finance, fitness, and digital tools where shape-based metrics drive decisions. With mobile search penetration high across the U.S., people are actively exploring how foundational shapes influence real-world applications, from app interfaces to interior planning. Before diving into the math, it’s important to understand the core: a circle with radius 5 units offers a base of consistent geometry, making approximations both accessible and reliable. The central angle—defined as the angle formed at the circle’s center—plays a key role. With 360 degrees in a full circle, 120 degrees represents a significant portion—exactly one-third of the whole, a fact that simplifies proportional thinking. To find the sector area, multiply the total circle area by the sector’s percentage of the full circle. The formula starts with the full circle’s area, πr², where r = 5. This gives 25π square units. Since 120 degrees is 1/3 of 360, the sector area becomes 25π ÷ 3, or approximately 26.18 square units when calculated numerically.