# High School Math : How to find circumference

## Example Questions

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### Example Question #61 : Radius

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

Circumference is given by the equation . We can use this equation with the given radius, 4.2, to solve for the circumference. ### Example Question #1 : 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?     Explanation:

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 13π in2 is centered at point C. What is the circumference of this circle?

13π

26π

√13π

√26π

2√13π

2√13π

Explanation:

The formula for the area of a circle is πr2.

We are given the area, and by substitution we know that 13π πr2.

We divide out the π and are left with 13 = r2.

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

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

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

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

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

8π

6π

25π

10π

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 #7 : 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? 96 ft

4π + 24

40 ft.

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 #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?

2.5π

π√2.5

π√5

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 #4 : 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 #3 : How To Find Circumference 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?      The equation for the circumference of a circle is , so by substituting the given radius into the equation, we get . 