Math Problem Statement
ind the radius r of the circle if an arc of length 6 m on the circle subtends a central angle of 3𝜋/7 rad. (Round your answer to two decimal places.)
Solution
To find the radius of the circle, you can use the formula relating the arc length , the radius , and the central angle (in radians):
Given:
- Arc length, m
- Central angle, rad
We need to find the radius . Rearrange the formula to solve for :
Substitute the values:
Now, calculate and round to two decimal places:
So, the radius is approximately 4.46 meters.
Would you like further details or have any questions?
Here are 5 related questions for you to explore:
- How would the radius change if the central angle were doubled?
- What is the formula for arc length if the angle is given in degrees?
- How do you convert a central angle from radians to degrees?
- What is the relationship between the circumference of a circle and the central angle for a full circle?
- How would the radius change if the arc length were halved?
Tip: Always ensure the central angle is in radians when using the arc length formula.
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Math Problem Analysis
Mathematical Concepts
Geometry
Circle Geometry
Formulas
Arc length formula: s = r * theta
Theorems
-
Suitable Grade Level
High School
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