# Common Core: 7th Grade Math : Know and Use the Formulas for the Area and Circumference of a Circle: CCSS.Math.Content.7.G.B.4

## Example Questions

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### Example Question #1 : How To Find Circumference

What is the circumference of a circle with a radius equal to ?

Explanation:

The circumference can be solved using the following equation:

### Example Question #2 : How To Find Circumference

The radius of a circle is . Give the circumference of the circle in terms of .

Explanation:

The circumference can be calculated as , where is the radius of the circle.

### Example Question #1 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

The area of a circle is . Give the circumference  of the circle in terms of .

Let .

Explanation:

The area of a circle can be calculated as , where   is the radius of the circle.

The circumference can be calculated as , where is the radius of the circle.

### Example Question #4 : How To Find Circumference

What is the circumference of a circle with a radius of ?

Explanation:

The circumference can be solved using the following equation:

Where  represents the radius. Therefore, when we substitute our radius in we get:

### Example Question #5 : How To Find Circumference

The perimeter of a given rectangle is equal to the circumference of a given circle. The circle has radius  inches; the width of the rectangle is  inches. What is the length of the rectangle?

inches

inches

inches

inches

inches

inches

Explanation:

The circumference of a circle with radius  inches is

inches.

The perimeter of the rectangle is therefore  inches. To find its length, substitute  and  into the equation and solve for :

inches

### Example Question #7 : Radius

What is the area of a circle that has a diameter of inches?

Explanation:

The formula for finding the area of a circle is . In this formula, represents the radius of the circle.  Since the question only gives us the measurement of the diameter of the circle, we must calculate the radius.  In order to do this, we divide the diameter by .

Now we use for in our equation.

### Example Question #5 : Area Of A Circle

What is the area of a circle with a diameter equal to 6?

Explanation:

Then, solve for area:

### Example Question #2 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

The diameter of a circle is . Give the area of the circle.

Explanation:

The area of a circle can be calculated using the formula:

,

where is the diameter of the circle, and is approximately .

### Example Question #7 : Area Of A Circle

The diameter of a circle is . Give the area of the circle in terms of .

Explanation:

The area of a circle can be calculated using the formula:

,

where   is the diameter of the circle and is approximately .

### Example Question #3 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

The radius of a circle is  . Give the area of the circle.

Explanation:

The area of a circle can be calculated as , where   is the radius of the circle, and is approximately .

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