### All High School Math Resources

## 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?

**Possible Answers:**

10*π*

6*π*

25*π*

8*π*

12*π*

**Correct answer:**

10*π*

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 = 10*π*.

### 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?

**Possible Answers:**

40 ft.

96 ft

4π + 24

8π + 24

**Correct answer:**

8π + 24

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?

**Possible Answers:**

π√5

π√2.5

5π

2.5π

None of the other answers

**Correct answer:**

π√5

We first must calculate the distance between these two points. Recall that the distance formula is:√((x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{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?

**Possible Answers:**

**Correct answer:**

The formula for the area of a circle is πr^{2}. For this particular circle, the area is 81π, so 81π = πr^{2}. Divide both sides by π and we are left with r^{2}=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 .

**Possible Answers:**

Not enough information to solve

**Correct answer:**

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)?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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

### Example Question #71 : Radius

Find the circumference of the following circle:

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

500π

3600π

600π

300π

**Correct answer:**

600π

If the radius is 18 inches, the diameter is 3 feet. The circumference of the tire is therefore 3π by C=d(π). After 200 revolutions, the tire and car have gone 3π x 200 = 600π feet.

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