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 Circumference

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

Possible Answers:

10π

6π

25π

8π

12π

Correct answer:

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 #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?

 
   

 

 Screen_shot_2013-03-18_at_4.54.03_pm

                 

 

 

Possible Answers:

40 ft.

96 ft

4π + 24

8π + 24

Correct answer:

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 #1 : 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:

π√5

π√2.5

2.5π

None of the other answers

Correct answer:

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 #1 : How To Find Circumference

If a circle has an area of , what is the circumference of the circle?

Possible Answers:

Correct answer:

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 #71 : Radius

Circle_with_radius

Find the circumference of a circle with a radius of .

Possible Answers:

Not enough information to solve

Correct answer:

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.Circle

What is the circumference of the circle (cm)?

Possible Answers:

Correct answer:

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?

Possible Answers:

Correct answer:

Explanation:

The equation for the circumference of a circle is , so by substituting the given radius into the equation, we get .

Example Question #71 : Radius

A circle has a diameter of 13 cm.  What is the circle's circumference?

Possible Answers:

Correct answer:

Explanation:

To find the circumference of a circle, multiply the circle's diameter by .

Example Question #71 : Radius

Find the circumference of the following circle:

21

Possible Answers:

 

Correct answer:

 

Explanation:

The formula for the circumference of a circle is

,

where  is the radius of the circle.

Plugging in our values, we get:

Example Question #92 : Circles

A car tire has a radius of 18 inches. When the tire has made 200 revolutions, how far has the car gone in feet?

Possible Answers:

500π

3600π

600π

300π

Correct answer:

600π

Explanation:

If the radius is 18 inches, the diameter is 3 feet. The circumference of the tire is therefore 3π by C=d(π). After 200 revolutions, the tire and car have gone 3π x 200 = 600π feet.

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