Recall that the length of an arc is merely a percentage of the circumference. The circumference is found by the equation:

For our data, this is:

Now the percentage for our arc is based on the angle and the total degrees in a circle, namely, .

So, the length of the arc is:

Recall that the length of an arc is merely a percentage of the circumference. The circumference is found by the equation:

For our data, this is:

Now the percentage for our arc is based on the angle and the total degrees in a circle, namely, .

So, the length of the arc is:

If the area of the circle is , the radius can be found using the formula for the area of a circle:

For our data, this is:

Therefore,

Now, the circumference of the circle is defined as:

For our data, this is:

Now, we know that a sector is a percentage of the total area. This percentage is easily calculated:

So, the length of the arc will merely be the same percentage, but now applied to the circumference:

Remember that the total degree measure of a circle is . This means that if you have parts into which you have divided your circle, each spoke must be or apart.

If the area of the circle is , the radius can be found using the formula for the area of a circle:

For our data, this is:

Therefore,

Now, the circumference of the circle is defined as:

For our data, this is:

Now, we know that a sector is a percentage of the total area. This percentage is easily calculated:

So, the length of the arc will merely be the same percentage, but now applied to the circumference:

Remember that the total degree measure of a circle is . This means that if you have parts into which you have divided your circle, each spoke must be or apart.

The only information provided is that the sector is . When finding a percent, it's helpful to remember that percents are a clean way to show fractions—that is portions—of a whole. In order to solve for what percent the sector makes of the entire circle, we need to find out what fractionthe sector makes up of the entire circle.

Keep in mind that a circle measures degrees. This means that the sector is of the total . This can be written out as:

This can be simplified to:

Note that the degrees signs are gone. This is because when you divide degrees by degrees, the units cancel out! This simplified fraction means that was three-fourths of the entire circle. Now, this fraction may be turned into a percent.

In order to go from fractions to percents, it's helpful to keep in mind that decimals are the important intermediate step. That is, as soon as a fraction can be turned into decimal form, it can easily be converted into a percent by multiplying by .

That is, the sector makes up of the entire circle.

The only information provided is that the sector is . When finding a percent, it's helpful to remember that percents are a clean way to show fractions—that is portions—of a whole. In order to solve for what percent the sector makes of the entire circle, we need to find out what fractionthe sector makes up of the entire circle.

Keep in mind that a circle measures degrees. This means that the sector is of the total . This can be written out as:

This can be simplified to:

Note that the degrees signs are gone. This is because when you divide degrees by degrees, the units cancel out! This simplified fraction means that was three-fourths of the entire circle. Now, this fraction may be turned into a percent.

In order to go from fractions to percents, it's helpful to keep in mind that decimals are the important intermediate step. That is, as soon as a fraction can be turned into decimal form, it can easily be converted into a percent by multiplying by .

That is, the sector makes up of the entire circle.

The only information provided is that the sector is . When finding a percent, it's helpful to remember that percents are a clean way to show fractions—that is, portions—of a whole.

Therefore, in order to solve for what percent the sector represents of the entire circle, we need to find out what fractionthe sector makes up of the entire circle. Keep in mind that a circle measures up to . This means that the sector is of the total . This can be written out as:

This can be simplified to:

Note that the degrees signs are gone. This is because when you divide degrees by degrees, the units cancel out! This simplified fraction means that was one-fifth of the entire circle. Now, this fraction may be turned into a percent.

In order to go from fractions to percents, it's helpful to keep in mind that decimals are the important intermediate step. That is, as soon as a fraction can be turned into decimal form, it can easily be converted into a percent by multiplying by 100.

That is, the sector makes up of the entire circle.

The only information provided is that the sector is . When finding a percent, it's helpful to remember that percents are a clean way to show fractions—that is, portions—of a whole.

Therefore, in order to solve for what percent the sector represents of the entire circle, we need to find out what fractionthe sector makes up of the entire circle. Keep in mind that a circle measures up to . This means that the sector is of the total . This can be written out as:

This can be simplified to:

Note that the degrees signs are gone. This is because when you divide degrees by degrees, the units cancel out! This simplified fraction means that was one-fifth of the entire circle. Now, this fraction may be turned into a percent.

In order to go from fractions to percents, it's helpful to keep in mind that decimals are the important intermediate step. That is, as soon as a fraction can be turned into decimal form, it can easily be converted into a percent by multiplying by 100.

That is, the sector makes up of the entire circle.