A circular arc has measure 4 cm and is intercepted by a central angle of pie over 6 radians. Find the radius r of the circle
We can use the formula for arc length:
L = rθ
where L is the length of the arc, r is the radius of the circle, and θ is the measure of the central angle in radians.
In this problem, we have L = 4 cm and θ = π/6 radians. Substituting these values into the formula, we get:
4 = r(π/6)
Multiplying both sides by 6/π, we get:
4(6/π) = r
Simplifying, we get:
r = 24/π
So the radius of the circle is 24/π cm.
Covert -144.44• to radian measure round your and otp the nearest hundredo
Covert -144.45• to radian measure round your answer to the nearest hundredth
To find the radius of a circle, we can use the formula:
Circumference of the circle = 2πr,
where r is the radius.
In this case, we have a circular arc with a measure of 4 cm, which means it represents a fraction of the entire circumference of the circle. The central angle that intercepts the arc has a measure of π/6 radians.
The formula to find the circumference of a circle using the central angle (θ) and the radius (r) is:
Circumference of the circle = θr,
where θ is the central angle.
We know that the length of the circular arc is 4 cm, so the circumference of the circle is also 4 cm.
Therefore, we can set up the equation:
4 = (π/6)r.
To solve for r, we can rearrange the equation:
r = (4 * 6) / π.
r = 24 / π.
Hence, the radius of the circle is 24 / π cm.