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High School Math : Circles

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Example Questions

Example Question #3 : How To Find Circumference

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

Possible Answers:

8π

10π

6π

12π

25π

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.

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Example Question #2 : 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

8π + 24

4π + 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.

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Example Question #3 : 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

2.5π

None of the other answers

π√2.5

5π

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.

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Example Question #1 : How To Find Circumference

If a circle has an area of $81\pi$ , what is the circumference of the circle?

Possible Answers:

$90\pi$

$81\pi$

$27\pi$

$18\pi$

$9\pi$

Correct answer:

$18\pi$

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.

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Example Question #3 : How To Find Circumference

Circle_with_radius

Find the circumference of a circle with a radius of r=3.5cm .

Possible Answers:

$\dpi{100} 7 \pi^{2} cm$

Not enough information to solve

$\dpi{100} 3.5 \pi cm$

$7 \pi cm$

$\dpi{100} 7 cm$

Correct answer:

$7 \pi cm$

Explanation:

In order to find the circumference, we will use the formula $C=2\pi r$ .

$C=2\pi r$

$C=2*\pi*3.5cm$

$\rightarrow 7 \pi cm$

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Example Question #101 : Circles

This figure is a circle with a radius of 3 cm. Circle

What is the circumference of the circle (cm)?

Possible Answers:

$12\pi$

$9\pi$

$3\pi$

$27\pi$

$6\pi$

Correct answer:

$6\pi$

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 ( $2\cdot3\cdot\pi=6\pi$ ).

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Example Question #2 : How To Find Circumference

What is the circumference of a circle with a radius of 4?

Possible Answers:

$14\Pi$

$8\Pi$

$24\Pi$

$4\Pi$

$16\Pi$

Correct answer:

$8\Pi$

Explanation:

The equation for the circumference of a circle is $2\Pi r$ , so by substituting the given radius into the equation, we get $8\Pi$ .

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Example Question #102 : Circles

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

Possible Answers:

40.84

20.41

26.75

53.5

134.45

Correct answer:

40.84

Explanation:

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

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Example Question #12 : How To Find Circumference

Find the circumference of the following circle:

Possible Answers:

$14 \pi\ m$

$12 \pi\ m$

$10 \pi\ m$

$8 \pi\ m$

$16 \pi\ m$

Correct answer:

$14 \pi\ m$

Explanation:

The formula for the circumference of a circle is

$C = 2 \pi (r)$ ,

where is the radius of the circle.

Plugging in our values, we get:

$C = 2\pi (7\ m)$

$C = 14 \pi\ m$

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Example Question #45 : Radius

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:

300π

3600π

600π

500π

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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High School Math : Circles

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #3 : How To Find Circumference

Example Question #2 : How To Find Circumference

Example Question #3 : How To Find Circumference

Example Question #1 : How To Find Circumference

Example Question #3 : How To Find Circumference

Example Question #101 : Circles

Example Question #2 : How To Find Circumference

Example Question #102 : Circles

Example Question #12 : How To Find Circumference

Example Question #45 : Radius

All High School Math Resources

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