Which circle has a radius that measures 10 units?
10
D
20
F
10
OG
20
The Correct Answer and Explanation is :
The circle that has a radius measuring 10 units is labeled “10” (the first “10” in your options). To clarify the concept of radius and its significance in understanding circles, let’s delve into what a radius is and how it relates to other circle measurements.
Understanding Radius
A radius is a line segment that connects the center of a circle to any point on its circumference. It is half the diameter of the circle, which is the distance across the circle passing through the center. If a circle has a radius of 10 units, this means that the distance from the center to any point on the edge of the circle is 10 units.
Characteristics of the Circle
With a radius of 10 units, we can calculate other important properties of the circle:
- Diameter: The diameter is twice the radius. Therefore, for a circle with a radius of 10 units, the diameter would be:
[
\text{Diameter} = 2 \times \text{Radius} = 2 \times 10 = 20 \text{ units}
] - Circumference: The circumference is the total distance around the circle. It can be calculated using the formula:
[
\text{Circumference} = 2\pi r
]
Where ( r ) is the radius. Plugging in the value:
[
\text{Circumference} = 2\pi \times 10 \approx 62.83 \text{ units}
] - Area: The area of the circle can be found using the formula:
[
\text{Area} = \pi r^2
]
For a radius of 10 units:
[
\text{Area} = \pi \times (10)^2 \approx 314.16 \text{ square units}
]
Conclusion
Identifying which circle has a radius of 10 units is crucial for solving problems related to geometry. The properties calculated from the radius—diameter, circumference, and area—are essential in various applications, from engineering to everyday tasks like determining the amount of material needed to cover a circular area. Thus, the circle labeled “10” has a radius of 10 units, allowing us to explore these geometric properties further.