### All High School Math Resources

## Example Questions

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

A circle has radius . What is the circumference, rounded to the nearest tenth?

**Possible Answers:**

**Correct answer:**

Circumference is given by the equation . We can use this equation with the given radius, 4.2, to solve for the circumference.

### Example Question #2 : How To Find Circumference

What is the circumference of a circle with a radius of 12?

What is the circumference of a circle with a radius of 12?

**Possible Answers:**

**Correct answer:**

To find the circumference of a circle given the radius we must first know the equation for the circumference of a circle which is

We then plug in the number for the radius into the equation yielding

We multiply to find the value for the circumference is .

The answer is .

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

A circle with an area of 13*π* in^{2} is centered at point *C*. What is the circumference of this circle?

**Possible Answers:**

√26*π*

26*π*

√13*π*

13*π*

2√13*π*

**Correct answer:**

2√13*π*

The formula for the area of a circle is *A *= *πr*^{2}.

We are given the area, and by substitution we know that 13*π *= *πr*^{2}.

We divide out the *π* and are left with 13 = *r*^{2}.

We take the square root of *r* to find that *r* = √13.

We find the circumference of the circle with the formula *C *= 2*πr*.

We then plug in our values to find *C *= 2√13*π*.

### 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:**

12*π*

25*π*

8*π*

10*π*

6*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:**

8π + 24

4π + 24

40 ft.

96 ft

**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 #2 : 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:**

5π

π√2.5

None of the other answers

2.5π

π√5

**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 : Circumference Of A Circle

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 #1 : How To Find Circumference

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 #71 : Radius

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 .