Circumference - HiSET

A circle with radius 20 has as its circumference times this, or

There are 360 degrees in a circle, so a 270-degree arc is

of the circle. Therefore, the length of this arc is

,

so a reasonable estimate of the length of this arc is

Of the five choices, 95 comes closest to the correct length.

We must first rewrite the equation of the circle in standard form

;

will be the radius.

Subtract 9 from both sides, and rearrange the terms remaining on the left as follows:

Note that blanks have been inserted after the linear terms. In these blanks, complete two perfect square trinomials by dividing linear coefficients by 2 and squaring:

Add to both sides, as follows:

Rewrite the expression on the left as the sum of the squares of two binomials.

The equation is now in standard form.

The radius is the square root of this, or

The circumference of a circle is the radius multiplied by , so

,

the correct response.

The equation, in standard form, of a circle on the coordinate plane with center and radius is

.

It is necessary to find the center and the radius of the circle in order to determine its equation.

The center of the circle is the midpoint of a given diameter. The midpoint of a segment with endpoints and can be found by applying the midpoint formula:

Setting :

Setting

The midpoint, and the center of the circle, is at .

The radius of the circle is the distance from the center to an endpoint, so we can use the distance formula

.

Substitute :

and

Now, set in the standard form of the equation of a circle, and the result is

The equation, in standard form, of a circle on the coordinate plane with center and radius is

.

It is necessary to find the center and the radius of the circle in order to determine its equation. The radius of the circle can be determined by applying the distance formula to the coordinates of the endpoints of the radius. However, it is not clear from the information given which endpoint is the center of the circle. Therefore, while can be determined, cannot. The correct response is that insufficient information exists to determine its equation.

Step 1: Since we are given the area, let's first find the radius of the circle.

If the area of a circle is calculated by: , we can plug in the values that are given to us. .

We have . We will divide by .

. To find the radius, we will take the square root of both sides.

So, .

Step 2: Now that we have the radius, we will now find the circumference.

The circumference formula by using the radius is .

Plug in all the information that we have...

The radius of the circle is the distance between its center and a point that it passes through. This radius can be calculated using the distance formula:

.

Setting :

The circumference of a circle is equal to multiplied by the radius, so

,

the correct response.

The standard form of the equation of a circle with center at and radius is

The circumference of the circle is ; to find the radius, divide this circumference by :

Now, set in the equation of the circle:

Simplifying:

,

the correct equation.

The standard form of the equation of a circle with center at and radius is

The area of the circle is ; to find the radius, substitute in the formula:

We do not need to find . Set in the equation of the circle:

Simplifying:

,

the correct equation.

A circle's circumference is calculated using the following formula:

In this equation, the variable, , is the circle's radius.

In our problem we are given the diameter. The diameter is related to the radius in the following manner:

Let's rewrite our formula by substituting the diameter for the radius.

Let's substitute and solve.

A circle with radius 20 has as its circumference times this, or

There are 360 degrees in a circle, so a 270-degree arc is

of the circle. Therefore, the length of this arc is

,

so a reasonable estimate of the length of this arc is

Of the five choices, 95 comes closest to the correct length.

We must first rewrite the equation of the circle in standard form

;

will be the radius.

Subtract 9 from both sides, and rearrange the terms remaining on the left as follows:

Note that blanks have been inserted after the linear terms. In these blanks, complete two perfect square trinomials by dividing linear coefficients by 2 and squaring:

Add to both sides, as follows:

Rewrite the expression on the left as the sum of the squares of two binomials.

The equation is now in standard form.

The radius is the square root of this, or

The circumference of a circle is the radius multiplied by , so

,

the correct response.

The equation, in standard form, of a circle on the coordinate plane with center and radius is

.

It is necessary to find the center and the radius of the circle in order to determine its equation.

The center of the circle is the midpoint of a given diameter. The midpoint of a segment with endpoints and can be found by applying the midpoint formula:

Setting :

Setting

The midpoint, and the center of the circle, is at .

The radius of the circle is the distance from the center to an endpoint, so we can use the distance formula

.

Substitute :

and

Now, set in the standard form of the equation of a circle, and the result is

The equation, in standard form, of a circle on the coordinate plane with center and radius is

.

It is necessary to find the center and the radius of the circle in order to determine its equation. The radius of the circle can be determined by applying the distance formula to the coordinates of the endpoints of the radius. However, it is not clear from the information given which endpoint is the center of the circle. Therefore, while can be determined, cannot. The correct response is that insufficient information exists to determine its equation.

Step 1: Since we are given the area, let's first find the radius of the circle.

If the area of a circle is calculated by: , we can plug in the values that are given to us. .

We have . We will divide by .

. To find the radius, we will take the square root of both sides.

So, .

Step 2: Now that we have the radius, we will now find the circumference.

The circumference formula by using the radius is .

Plug in all the information that we have...

The radius of the circle is the distance between its center and a point that it passes through. This radius can be calculated using the distance formula:

.

Setting :

The circumference of a circle is equal to multiplied by the radius, so

,

the correct response.

The standard form of the equation of a circle with center at and radius is

The circumference of the circle is ; to find the radius, divide this circumference by :

Now, set in the equation of the circle:

Simplifying:

,

the correct equation.

The standard form of the equation of a circle with center at and radius is

The area of the circle is ; to find the radius, substitute in the formula:

We do not need to find . Set in the equation of the circle:

Simplifying:

,

the correct equation.

A circle's circumference is calculated using the following formula:

In this equation, the variable, , is the circle's radius.

In our problem we are given the diameter. The diameter is related to the radius in the following manner:

Let's rewrite our formula by substituting the diameter for the radius.

Let's substitute and solve.

A circle with radius 20 has as its circumference times this, or

There are 360 degrees in a circle, so a 270-degree arc is

of the circle. Therefore, the length of this arc is

,

so a reasonable estimate of the length of this arc is

Of the five choices, 95 comes closest to the correct length.