High School Math : Circles

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : 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?

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         Circle X

 

 

Possible Answers:

4

7

√12

6

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 #6 : 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:

4.70 inches

5.43 inches

14.75 inches

3.06 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 #111 : Geometry

If the circumference of a circle is , what is the radius?

Possible Answers:

Correct answer:

Explanation:

The formula for circumference is .

Plug in our given information.

Divide both sides by .

Example Question #62 : Radius

Find the radius of a circle with area

Possible Answers:

Correct answer:

Explanation:

Since the formula for the area of a triangle is 

plug in the given area and isolate for . This yields 13. 

Example Question #63 : Radius

The circumference of a circle is 45 inches.  The circle's radius is ____ inches.

Possible Answers:

Correct answer:

Explanation:

When you know the circumference of a circle, you can determine its diameter by dividing the circumference by .  Then, when you have the diameter, you can determine the radius by dividing 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? 

Possible Answers:

8

5

16

4

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 #1 : How To Find The Length Of A Radius

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

Possible Answers:

24.5 inches

7 inches

14 inches

16 inches

49 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

Example Question #1 : How To Find Circumference

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

Possible Answers:

Correct answer:

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 #121 : Plane Geometry

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:

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?

Possible Answers:

26π

2√13π

13π

√13π

√26π

Correct answer:

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.

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