Circles - GED Math

The circumference of the circle is the sum of the lengths of the arcs, which is

.

The white sector has degree measure

.

The radius of the circle can be found using the circumference formula, setting :

The area of the white sector is therefore

.

There are a total of 360 degrees to a complete circle. The shaded sector has degree measure , so the unshaded sector has degree measure

Also, a sector of is of the circle, so, setting , we find that the unshaded sector is

of the circle. This reduces to

,

the correct percentage.

There are a total of in a circle. The unshaded portion of the circle represents a sector, so the shaded portion represents a sector of measure

.

This sector represents

of the circle.

What percentage of a circle is covered by a sector with a central angle of ?

To find the percentage of a circle from the central angle, we need to use the following formula:

Where theta is our central angle.

Plug in our given degree measurement and simplify.

So, our answer is 66.67%

The total number of degrees in a circle is , so the shaded sector represents of the circle. In terms of percent, this is

.

The shaded sector is 40% if the circle, so the unshaded sector is of the circle.

Recall that the length of an arc is a proportion of the circumference, just like how the measure of a central angle is a proportion of the total number of degrees in a circle.

Thus, we can write the following equation to solve for arc length.

Plug in the given central angle and circumference to find the length of the minor arc .

The radius of a circle, given its area , can be found using the formula

Set :

Find by dividing both sides by and then taking the square root of both sides:

The circumference of this circle is found using the formula

:

A arc of the circle is one fourth of the circle, so the length of the arc is

If a sector covers of the area of a given circle, what is the measure of that sector's central angle?

While this problem may seem to not have enough information to solve, we actually have everything we need.

To find the measure of a central angle, we don't need to know the actual area of the sector or the circle. Instead, we just need to know what fraction of the circle we are dealing with. In this case, we are told that the sector represents four fifths of the circle.

All circles have 360 degrees, so if our sector is four fifths of that, we can find the answer via the following.

So our answer is:

The diameter of a circle is twice the radius:

Plug in the radius value:

The radius is half of the diameter, or 11.

The radius is half of the diameter:

From here we plug in our diameter measure of 12 and solve for the radius:

The diameter is twice the radius:

The equation for circumference of a circle is as follows:

Plug in the given values and solve for the radius:

Now we divide each side by :

We know the equation for the circumference of a circle is . We also know that the the diameter is the twice the radius, so we can write .

Plug in the given values and solve:

In order to solve this question, start by finding the radius. Recall that the area of a circle is computed as:

For our data, this is:

Solving for , we get:

or

Now, recall that the diameter is double the radius. Thus, it is .

Recall that the circumference formula is:

Now, for your data, this gives you:

You need to be careful, for some students get confused when they have to divide by . However, just treat it like any other number or variable. This means that you can solve for and get:

Write the area formula of a circle.

Substitute the area.

Divide by pi on both sides.

Square root both sides.

The radius is:

The diameter is double the radius.

The answer is:

Write the formula for the area of a circle.

Substitute the area into the equation.

Divide by pi on both sides.

The diameter is twice the radius.

The answer is:

There are three feet in one yard.

Using dimensional analysis, we can determine the given diameter in yards first.

The radius is half the diameter.

The answer is: