# High School Math : Circles

## Example Questions

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

A 6 by 8 rectangle is inscribed in a circle. What is the circumference of the circle?

10π

6π

25π

8π

12π

10π

Explanation:

First you must draw the diagram. The diagonal of the rectangle is also the diameter of the circle. The diagonal is the hypotenuse of a multiple of 2 of a 3,4,5 triangle, and therefore is 10.
Circumference = π * diameter = 10π.

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

A gardener wants to build a fence around their garden shown below. How many feet of fencing will they need, if the length of the rectangular side is 12 and the width is 8?

40 ft.

96 ft

4π + 24

8π + 24

8π + 24

Explanation:

The shape of the garden consists of a rectangle and two semi-circles. Since they are building a fence we need to find the perimeter. The perimeter of the length of the rectangle is 24. The perimeter or circumference of the circle can be found using the equation C=2π(r), where r= the radius of the circle. Since we have two semi-circles we can find the circumference of one whole circle with a radius of 4, which would be 8π.

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

The diameter of a circle is defined by the two points (2,5) and (4,6). What is the circumference of this circle?

π√5

π√2.5

2.5π

π√5

Explanation:

We first must calculate the distance between these two points. Recall that the distance formula is:√((x2 - x1)2 + (y2 - y1)2)

For us, it is therefore: √((4 - 2)2 + (6 - 5)2) = √((2)2 + (1)2) = √(4 + 1) = √5

If d = √5, the circumference of our circle is πd, or π√5.

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

If a circle has an area of , what is the circumference of the circle?

Explanation:

The formula for  the area of a circle is πr2. For this particular circle, the area is 81π, so 81π = πr2. Divide both sides by π and we are left with r2=81. Take the square root of both sides to find r=9. The formula for the circumference of the circle is 2πr = 2π(9) = 18π. The correct answer is 18π.

### Example Question #71 : Radius

Find the circumference of a circle with a radius of .

Not enough information to solve

Explanation:

In order to find the circumference, we will use the formula .

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

This figure is a circle with a radius of 3 cm.

What is the circumference of the circle (cm)?

Explanation:

In order to find the circumference of a circle (which is the perimeter or distance around the circle), you must double the radius and multiply by pi ().

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

What is the circumference of a circle with a radius of 4?

Explanation:

The equation for the circumference of a circle is , so by substituting the given radius into the equation, we get .

### Example Question #71 : Radius

A circle has a diameter of 13 cm.  What is the circle's circumference?

Explanation:

To find the circumference of a circle, multiply the circle's diameter by .

### Example Question #71 : Radius

Find the circumference of the following circle:

Explanation:

The formula for the circumference of a circle is

,

where  is the radius of the circle.

Plugging in our values, we get:

### Example Question #92 : Circles

A car tire has a radius of 18 inches. When the tire has made 200 revolutions, how far has the car gone in feet?

500π

3600π

600π

300π