Area of a sector of a circle?

Consider a circle of radius ##8## centimetres. Recall that the centre angle in a circle is always ##360˚##. However, a semi-circle is a circle cut in half. Hence, the centre angle for the semi-circle is cut in half, or has a measure of ##180˚##.

Here's a diagram of what's going on.

Before applying the formula, let's convert ##180˚## to radians.

##(180˚)/1 xx pi/(180˚) = pi##

We will now use the formula to determine the area of this semi-circle.

##A = 1/2 xx pi xx 8^2##

##A = 1/2 xx pi xx 64##

##A = 32pi " cm^2##

We can confirm this using the formula for area of a semi-circle, ##A = (r^2pi)/2##.

##A = (8^2pi)/2##

##A = 32 pi" cm^2##

Same, so both formulae work.

Here are a few problems for you practice.

Practice exercises:

Determine the area of the following semi-circles.

a) The semi-circle contained inside a circle of radius ##5## inches.

b) The semi-circle contained inside a circle of diameter ##22## feet.

c) The semi-circle contained inside a circle of circumference ##18## meters.

Hopefully this helps, and good luck!