In a circle whose radius is 13 cm, a central angle intercepts an arc that measures 65o. What is the arc length? Round your answer to the nearest hundredth of a centimeter.
Why did the circle want to measure its arc length? Because it wanted to be "a-cute" mathematician!
In all seriousness, to find the arc length, you need to use the formula L = rθ, where L is the arc length, r is the radius, and θ is the central angle in radians.
First, we need to convert the central angle from degrees to radians. Since there are 2π radians in a circle, we can use the conversion factor π radians / 180 degrees.
θ = 65 * π / 180
θ ≈ 1.1345 radians
Now we can plug the values into the formula:
L = 13 * 1.1345
L ≈ 14.74 cm
Therefore, the arc length is approximately 14.74 cm.
To find the arc length, we can use the formula:
Arc Length = (Central Angle / 360) * (2 * π * Radius)
Given:
Radius = 13 cm
Central Angle = 65o
Plugging in the values, we have:
Arc Length = (65 / 360) * (2 * π * 13)
Calculating,
Arc Length ≈ (0.180556) * (2 * 3.14159 * 13)
≈ (0.180556) * (6.28318 * 13)
≈ (0.180556) * (81.68134)
≈ 14.74044 cm
Therefore, the arc length is approximately 14.74 cm (rounded to the nearest hundredth of a centimeter).
To find the arc length, you need to use the formula:
Arc Length = (Central Angle / 360°) × Circumference
First, let's find the circumference of the circle. The formula for the circumference of a circle is:
Circumference = 2π × radius
In this case, the radius is 13 cm, so the circumference is:
Circumference = 2π × 13 cm
To find the arc length, we also need to know the central angle, which is given as 65°.
Now we can plug these values into the formula for arc length:
Arc Length = (65° / 360°) × (2π × 13 cm)
Simplify the expression:
Arc Length = 0.1805556 × (2π × 13 cm)
Using a calculator, multiply:
Arc Length ≈ 0.1805556 × 81.68 cm
Arc Length ≈ 14.76 cm
Therefore, the arc length, rounded to the nearest hundredth of a centimeter, is approximately 14.76 cm.