# High School Math : Radius

## Example Questions

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### Example Question #31 : Circles

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

Explanation:

To find the area of a circle you must plug the radius into  in the following equation.

In this case, the radius is , so we plug  into .

### Example Question #32 : Circles

What is the area of a circle with a radius of 9?

Explanation:

To find the area of a circle you must plug the radius into  in the following equation

In this case the radius is 9 so we plug it into  to get

We then multiply it by  to get our answer

### Example Question #33 : Circles

Find the area of a circle with a radius of .

Not enough information to solve

Explanation:

In order to find the circle's area, utilize the formula .

### Example Question #34 : Circles

A circle has a radius , what is its area?

Not enough information to solve

Explanation:

In order to find the circle's area, utilize the formula .

### Example Question #35 : Circles

A circle has a diameter , what is its area?

Not enough information to solve

Explanation:

In order to find the circle's area, utilize the formula .

However, we need to convert our diameter into a radius.

Solve for .

Insert the radius into the area formula and solve.

### Example Question #36 : Circles

Refer to the above drawing. This shows a ring-shaped garden with inner radius 20 feet and outer radius 40 feet. To the nearest square foot, what is the area of the garden?

Explanation:

The total area of the garden is the area of the outer circle -  - minus that of the inner circle - .

### Example Question #37 : Circles

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

Explanation:

To find the area of a circle you must plug the radius into the following equation

In this case the radius is  so we plug it in and square it to get

We then multiply it by  to get our answer

### Example Question #38 : Circles

Four circles are drawn inside of a square. What is the area of the shaded region?

Explanation:

Each set of two circles fits perfectly between the sides of the square. The diameters of two of the circle must equal the length of one side of the square.

Each side has a length of 8 and the diameter of a circle is twice the radius. We can use these relationships to substitute into the first equation.

The area of a circle can be calculated using the equation . The shaded region is made of four circles, all with the same radius.

The area of one circle is given below.

The area of the shaded region (four circles) would be .

### Example Question #39 : Circles

O, M, and I represent three circles. Each circle shares the same center point. What is the area of the shaded region?

Explanation:

The area of the shaded region can be found by using the areas of the individual circles. The area of the full figure is the area of circle O. The area of the center shaded area is the area of circle I. Circle M contains circle I. The area of the shaded region will be equal to .

First, find the area of each circle using .

Now we can substitute into our equation.

### Example Question #41 : Circles

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