Find The Length Of An Arc Of A Circle With Radius 12 Cm If The Arc Subtends A Central Angle Of 30°

Introduction

Finding the length of an arc of a circle can be a tricky problem to solve if you don’t know the right formula. But with some knowledge about circles and angles, anyone can solve this problem in no time. In this article, we will discuss how to find the length of an arc of a circle with radius 12 cm when it subtends a central angle of 30°. We’ll go over the formula for calculating arc length and then use it to solve our example question. Read on to learn more!

The basics of arcs and angles

To find the length of an arc, we need to know the radius of the circle and the central angle subtended by the arc. The central angle is measured in degrees and is the angle between two radii of a circle. The formula for calculating the length of an arc is:

Length of arc = Radius * Central Angle (in radians)

We can convert our central angle from degrees to radians using the following formula:

Central Angle (in radians) = Central Angle (in degrees) * (pi/180)

where pi is 3.14. Therefore, our final formula for finding the length of an arc is:

Length of arc = Radius * Central Angle (in degrees) * (pi/180)

How to calculate the length of an arc

Assuming that you already know the formula for the circumference of a circle, which is C = 2πr, calculating the length of an arc is simply a matter of plugging in the known values and solving for L. In this case, we know that the radius (r) is equal to 10 cm and that the central angle (θ) is equal to 30°. Plugging these values into the circumference formula gives us:

L = 2π(10 cm) * (30°/360°)

L = 2π(10 cm) * (0.083)

L = 0.541 cm

An example: finding the length of an arc with radius 12 cm and central angle 30°

To find the length of an arc with radius 12 cm and central angle 30°, we need to use the formula for the circumference of a circle:

C = 2πr

where C is the circumference, π is pi, and r is the radius. In our case, r = 12 cm. Therefore, the circumference of our circle is:

C = 2π(12)

C = 24π cm

Now that we have the circumference of the circle, we can find the length of our arc by dividing it by 360° to get the length of 1°, and then multiplying it by 30° to get the length of our specific arc:

length of arc = (24π cm)/360° * 30°

length of arc = 8π/3 cm

Conclusion

In this article, we discussed how to find the length of an arc with a given radius and central angle. Using the formula for arc length, we were able to determine that the length of an arc with a radius of 12 cm and subtending a central angle of 30° is 20.0 cm. We hope that this information has been helpful in solving your problem and encourage you to explore more problems related to angles, radii, and arcs on your own.