It is very easy to compute the angle of a sector if we know what it is as a percentage of the total circle.  To do this, you merely need to multiply  by ˚.  This yields ˚. 

It is very easy to compute the angle of a sector if we know what it is as a percentage of the total circle.  To do this, you merely need to multiply  by ˚.  This yields ˚

Let  be the radius of Circle B. The radius of Circle A is therefore .

A  sector of a circle comprises  of the circle. The  sector of circle A has area , the area of Circle B. The two quantities are equal.

To find the area of a sector, you need to find a percentage of the total area of the circle.  You do this by dividing the sector angle by the total number of degrees in a full circle (i.e. ˚).  Thus, for our circle, which has a sector with an angle of ˚, we have a percentage of:

Now, we will multiply this by the total area of the circle.  Recall that we find such an area according to the equation:

For our problem,

Therefore, our equation is:

Using your calculator, you can determine that this is approximately .

To find the area of a sector, you need to find a percentage of the total area of the circle.  You do this by dividing the sector angle by the total number of degrees in a full circle (i.e. ˚).  Thus, for our circle, which has a sector with an angle of ˚, we have a percentage of:

Now, we will multiply this by the total area of the circle.  Recall that we find such an area according to the equation:

For our problem, 

Therefore, our equation is:

Using your calculator, you can determine that this is approximately .

 has two angles of degree measure 45; the third angle must measure 90 degrees, making  a right triangle.

For the sake of simplicity, let ; the reasoning is independent of the actual length. The legs of a 45-45-90 triangle are congruent, so . The area of a right triangle is half the product of its legs, so 

Also, if , then the orange semicircle has diameter 1 and radius . Its area can be found by substituting  in the formula:

 has a greater area than the orange semicircle.

 has two angles of degree measure 60; its third angle must also have measure 60, making  an equilateral triangle 

For the sake of simplicity, let ; the reasoning is independent of the actual length. The area of equilateral  can be found by substituting  in the formula

Also, if , then the orange semicircle has diameter 1 and radius . Its area can be found by substituting  in the formula:

 has a greater area than the orange semicircle.

The radius of a circle is half its diameter; the radius of the circle in the diagram is half of 20, or 10.

To find the area of the circle, set  in the area formula:

The circle is divided into sixteen sectors of equal size, five of which are shaded; the shaded portion is

.

This question is asking for the length of an arc corresponding to  of a circle with radius eight feet. The question can be answered by evaluating for :

To compare  and , we note that

and 

We need to be able to compare  and . If we know which of the intercepting angles is the greater, then we know which of the arcs is greater. The intercepting angles are , respectively. However, we are not given this relationship.