Home > Geometry > Circle Arcs and Sectors

How do we express area of a sector of a circle in terms of angle in radians? What is the area of a semicircle using this?

Answer 1

Area of semicircle is #(pir^2)/2#

Radian describes an angle subtended by an arc of circle, whose length is equal to its radius. As circumference of a circle is #2pi# times radius, complete circle is #2pi# radians and a semicircle subtends an anglre of #pi# radians.

As area of a circle is given by #1/2r^2theta#, (where #theta# is in radians)

as semicircle subtendsan angle #pi# radians, its area is

#1/2r^2xxpi=(pir^2)/2#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Ella Armstrong

To express the area of a sector of a circle in terms of angle in radians, you use the formula:

Area of sector = (θ/2) * r^2

Where:

θ is the angle subtended by the sector in radians,
r is the radius of the circle.

For a semicircle, the angle subtended is π radians (since a semicircle spans half the circumference of the circle), so the area of a semicircle can be calculated using the formula:

Area of semicircle = (π/2) * r^2

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.