Question

If the circle has area 128cm² and radius 8 cm, what will its central angle?

a) Determine the formula relating the area of a circle to its central angle.
b) Calculate the central angle of the given circle using the provided information.
c) Explain the steps involved in finding the central angle.
d) Discuss any additional properties or concepts related to circles that are relevant.

Answer 1

To find the central angle of a circle, you can use the formula Central angle = (Area of sector / Area of circle) * 360 degrees. The central angle of the given circle with an area of 128cm² and radius of 8cm is 720 degrees. Additional properties of circles include the circumference and diameter.

Step-by-step explanation:

To find the central angle of a circle, we can use the formula:

Central angle = (Area of sector / Area of circle) * 360 degrees

In this case, the given area of the circle is 128cm² and the radius is 8cm. The formula for the area of a circle is A = πr², so the radius squared is 64cm². Therefore, the central angle can be calculated as:

Central angle = (128 / 64) * 360 degrees = 720 degrees.

The central angle of the given circle is 720 degrees.

Additional properties related to circles include the circumference and diameter. The circumference of a circle is given by the formula C = 2πr, where r is the radius. The diameter of a circle is twice the radius, so it can be calculated as D = 2r. These properties are useful in various applications of circles, such as finding the length of an arc or the distance around a circular track.