Basic Geometry : How to find the length of a radius

Study concepts, example questions & explanations for Basic Geometry

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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.

Possible Answers:

Correct answer:

Explanation:

The area of a circle is

Substitute 1 for :

This is the radius in yards. The radius in inches is 36 times this.

20.3 inches is the radius.

Example Question #2 : 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?

 

Possible Answers:

6

18

9

36

Correct answer:

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 #162 : Plane Geometry

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?

Act_math_170_02

         Circle X

 

 

Possible Answers:

7

√12

6

4

Correct answer:

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 #2 : 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? 

 

Possible Answers:

5.43 inches

14.75 inches

3.06 inches

4.70 inches

9.39 inches

Correct answer:

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 #162 : Plane Geometry

Circle_line_identity

What is the name of the segment in red?

Possible Answers:

Radius

Chord

Ray

Diagonal

Diameter

Correct answer:

Radius

Explanation:

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

Example Question #163 : Plane Geometry

Circle_line_identity

What is the name of the segment in brown?

Possible Answers:

Ray

Radius

Diagonal

Chord

Diameter

Correct answer:

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 #164 : Plane Geometry

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

Possible Answers:

Correct answer:

Explanation:

The radius is half of the diameter. To find the radius, simply divide the diameter by 2.

Example Question #3 : 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? 

Possible Answers:

4

5

8

16

Correct answer:

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 #165 : Plane Geometry

The circle shown below has an area equal to . What is the length of the radius, , of this circle?

Circle

Possible Answers:

Cannot be determined.

Correct answer:

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 #93 : Circles

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

Possible Answers:

24.5 inches

49 inches

14 inches

7 inches

16 inches

Correct answer:

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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