### All High School Math Resources

## Example Questions

### Example Question #1 : How To Find The Angle Of A Sector

What is the angle of a sector that has an arc length of on a circle of diameter ?

**Possible Answers:**

**Correct answer:**

The first thing to do for this problem is to compute the total circumference of the circle. Notice that you were given the diameter. The proper equation is therefore:

For your data, this means,

Now, to compute the angle, note that you have a percentage of the total circumference, based upon your arc length:

Rounded to the nearest hundredth, this is .

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

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

**Possible Answers:**

**Correct answer:**

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 #2 : How To Find The Area Of A Circle

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

**Possible Answers:**

**Correct answer:**

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 #3 : How To Find The Area Of A Circle

Find the area of a circle with a radius of .

**Possible Answers:**

Not enough information to solve

**Correct answer:**

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

### Example Question #4 : How To Find The Area Of A Circle

A circle has a radius , what is its area?

**Possible Answers:**

Not enough information to solve

**Correct answer:**

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

### Example Question #5 : How To Find The Area Of A Circle

A circle has a diameter , what is its area?

**Possible Answers:**

Not enough information to solve

**Correct answer:**

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 #6 : How To Find The Area Of A Circle

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?

**Possible Answers:**

**Correct answer:**

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

### Example Question #7 : How To Find The Area Of A Circle

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

**Possible Answers:**

**Correct answer:**

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 #8 : How To Find The Area Of A Circle

**Possible Answers:**

**Correct answer:**

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.

Solve for the radius, .

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 #9 : How To Find The Area Of A Circle

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

**Possible Answers:**

**Correct answer:**

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.