# Basic Geometry : How to find the length of a radius

## Example Questions

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### Example Question #1 : How To Find The Length Of A Radius

The area of a circle is one square yard. Give its radius in inches, to the nearest tenth of an inch.      Explanation:

The area of a circle is Substitute 1 for :  This is the radius in yards. The radius in inches is 36 times this. ### Example Question #1 : How To Find The Length Of A Radius

A circle has an area of 36π inches. What is the radius of the circle, in inches?

36

18

9

6

6

Explanation:

We know that the formula for the area of a circle is πr2. Therefore, we must set 36π equal to this formula to solve for the radius of the circle.

36π = πr2

36 = r2

6 = r

### Example Question #6 : How To Find The Length Of A Radius

Circle X is divided into 3 sections: A, B, and C. The 3 sections are equal in area. If the area of section C is 12π, what is the radius of the circle? Circle X

6

4

7

√12

6

Explanation:

Find the total area of the circle, then use the area formula to find the radius.

Area of section A = section B = section C

Area of circle X = A + B + C = 12π+ 12π + 12π = 36π

Area of circle =  where r is the radius of the circle

36π = πr2

36 = r2

√36 = r

6 = r

### Example Question #7 : How To Find The Length Of A Radius

The specifications of an official NBA basketball are that it must be 29.5 inches in circumference and weigh 22 ounces.  What is the approximate radius of the basketball?

4.70 inches

5.43 inches

3.06 inches

14.75 inches

9.39 inches

4.70 inches

Explanation:

To Find your answer, we would use the formula:  C=2πr. We are given that C = 29.5. Thus we can plug in to get  [29.5]=2πr and then multiply 2π to get 29.5=(6.28)r.  Lastly, we divide both sides by 6.28 to get 4.70=r.   (The information given of 22 ounces is useless)

### Example Question #1 : How To Find The Length Of A Radius

What is the name of the segment in red?

Diagonal

Diameter

Ray

Chord

Explanation:

The radius is the distance from the center of a circle to any point on it's perimeter.

### Example Question #1 : How To Find The Length Of A Radius

What is the name of the segment in brown?

Chord

Diameter

Diagonal

Ray

Chord

Explanation:

A chord is a line segment which joins two points on a curve. A chord does not go through the center of a circle.

### Example Question #4 : How To Find The Length Of A Radius

The diameter of a circle is 16 centimeters.  What is the circle's radius in centimeters?      Explanation:

The radius is half of the diameter. To find the radius, simply divide the diameter by 2. ### Example Question #1 : How To Find The Length Of A Radius

A circle with center (8, 5) is tangent to the y-axis in the standard (x,y) coordinate plane. What is the radius of this circle?

8

16

5

4

8

Explanation:

For the circle to be tangent to the y-axis, it must have its outer edge on the axis. The center is 8 units from the edge.

### Example Question #1 : How To Find The Length Of A Radius

The circle shown below has an area equal to . What is the length of the radius, , of this circle?   Cannot be determined.   Explanation:

The formula for the area of a circle is . We can fill in what we know, the area, and then solve for the radius, . Divide each side of the equation by : Take the square root of each side:  ### Example Question #1 : How To Find The Length Of A Radius

A circle has an area of . What is the radius of the circle, in inches?

24.5 inches

14 inches

16 inches

7 inches

49 inches

7 inches

Explanation:

We know that the formula for the area of a circle is πr2. Therefore, we must set 49π equal to this formula to solve for the radius of the circle.

49π = πr2

49 = r2

7 = r

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