Arc-length and sector area using formulas in degrees:
The ratio of a circle's perimeter to its diameter is constant in all circles. This constant is called π (pi). Since the diameter is twice the radius, the circumference of a circle is
The area of a circle is
where r is the radius of the circle.
An arc is part of the circumference of a circle. It is defined by the radius r of the circle and the angle θ that the arc "sweeps out" over the circle's perimeter.
Since the arc length is a fraction of the overall circumference determined by the value of the angle θ, the arc length is calculated as
A sector is an area enclosed between a circular arc and the two radii of the circle touching each end of the arc, like a slice of pizza.
The area of a circle is πr2, and there are 360 degrees of rotation in a circle. Therefore, a sector with central angle θ is 360∘θ of a full circle, and has area
Nice work completing Radians, arcs and sectors, here's a quick recap of what we covered:
Exercises checked off
Arc-length and sector area using formulas in degrees:
The ratio of a circle's perimeter to its diameter is constant in all circles. This constant is called π (pi). Since the diameter is twice the radius, the circumference of a circle is
The area of a circle is
where r is the radius of the circle.
An arc is part of the circumference of a circle. It is defined by the radius r of the circle and the angle θ that the arc "sweeps out" over the circle's perimeter.
Since the arc length is a fraction of the overall circumference determined by the value of the angle θ, the arc length is calculated as
A sector is an area enclosed between a circular arc and the two radii of the circle touching each end of the arc, like a slice of pizza.
The area of a circle is πr2, and there are 360 degrees of rotation in a circle. Therefore, a sector with central angle θ is 360∘θ of a full circle, and has area
Nice work completing Radians, arcs and sectors, here's a quick recap of what we covered:
Exercises checked off