# Pre-Algebra : Area of a Circle

## Example Questions

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### Example Question #1 : Area Of A Circle

A circle has a circumference of . What is its area?

Explanation:

To begin, we need to find the radius of the circle. The circumference of a circle is given as follows:

,

Then, a circle with circumference  will have the following radius:

Using the radius, we can now solve for the area:

The area of the circle is .

### Example Question #2 : Area Of A Circle

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

Explanation:

If the diameter is 7, then the radius is half of 7, or 3.5.

Plug this value for the radius into the equation for the area of a circle:

### Example Question #3 : Area Of A Circle

The rectangle in the above figure has length 20 and height 10. What is the area of the orange region?

Insufficient information is given to determine the area.

Explanation:

The orange region is a composite of two figures:

One is a rectangle measuring 20 by 10, which, subsequently, has area

.

The other is a semicircle with diameter 10, and, subsequently, radius 5. Its area is

.

### Example Question #1 : Area Of A Circle

A circle has a diameter of  inches. What is the area of the circle? Round to the nearest tenth decimal place.

Explanation:

The formula to find the area of a circle is .

First you must find the radius from the diameter.

In this case it is,

### Example Question #1 : How To Find The Area Of A Circle

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 #1 : How To Find The 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 : How To Find The Area Of A Circle

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 #3 : How To Find The 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 #5 : How To Find The Area Of A Circle

The circumference of a circle is inches. Find the area of the circle.

Let .

Explanation:

First we need to find the radius of the circle. The circumference of a circle is , where is the radius of the circle.

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

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

Find the area of a circle that has a radius of .