a circle with 4 inch radius, find length of arc when intercepted by central angle of 240 degrees
a circle has a radius of 4cm. Find the length of an arc subtended by a central angle of 150 degrees.
To find the length of the arc intercepted by a central angle of 240 degrees within a circle with a 4-inch radius, you can use the formula:
Arc Length = (Central Angle / 360) * 2 * π * Radius
Let's substitute the given values:
Arc Length = (240 / 360) * 2 * π * 4
Simplifying further:
Arc Length = (2/3) * 2 * π * 4
Arc Length = (4/3) * π * 4
Arc Length ≈ 16.85 inches
Therefore, the length of the arc intercepted by a central angle of 240 degrees within a circle with a 4-inch radius is approximately 16.85 inches.
To find the length of the arc intercepted by a central angle of 240 degrees in a circle with a radius of 4 inches, you can use the formula:
Arc Length = (Central Angle / 360 degrees) * Circumference
First, calculate the circumference of the circle using the formula:
Circumference = 2 * π * Radius
Plugging in the radius value of 4 inches, we have:
Circumference = 2 * π * 4 = 8π inches
Next, calculate the length of the arc by using the formula mentioned earlier:
Arc Length = (Central Angle / 360 degrees) * Circumference
Plugging in the central angle value of 240 degrees and the circumference value we just calculated, we have:
Arc Length = (240 / 360) * 8π
= (2/3) * 8π
= (16/3)π
So, the length of the arc intercepted by a central angle of 240 degrees in a circle with a 4-inch radius is (16/3)π inches, which is approximately 16.85 inches.
r=radius
θ=central angle in radians
To convert degrees to radians, multiply the number of degrees by π and divide by 180°.
Arc length, l = rθ
Example:
θ = 90°
=90*π/180=π/2
r = 10 m
Length of arc
= rθ
= 10 * π/2
= 5π
= 15.7 m