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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

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9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #106 : How To Find Circumference

Find the circumference of a circle whose diameter, , is 10.

Note: $\pi=3.14$

Possible Answers:

C=78.5

C=25

C=62.8

C=31.4

Correct answer:

C=31.4

Explanation:

The formula for circumference is

$C=2\pi r$ .

We were initially given diameter, so to get the radius we divide d by 2.

r=d/2=10/2=5 .

We then solve by saying

$C=2\pi r=2*3.14*5=31.4$

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Example Question #302 : Circles

The area of a circle is $4 \pi$ . What is the circumference?

Possible Answers:

$4 \pi$

$2 \pi$

$\pi$

Correct answer:

$4 \pi$

Explanation:

The area of a circle is $\pi r^2$ , so in this case the radius squared is 4. Since the square root of 4 is 2, the radius has length 2. To find the circumference, use the formula $2\pi r$ . In this case, $2 \pi \cdot 2 = 4 \pi$

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Example Question #301 : Circles

Circle radius

The radius of the circle shown here is units long. What is its circumference?

Possible Answers:

$16\pi$

$8\pi$

$12\pi$

$4\pi$

$10\pi$

Correct answer:

$8\pi$

Explanation:

The formula for the circumference of a circle given its radius is $C=2\pi r$ . For the circle given in the problem, r=4 units, and so

$C=2\pi r = 2\pi (4)=8\pi$ .

Hence, the circumference of this circle is $8\pi$ units.

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Example Question #301 : Radius

A circle has diameter 20.

True or false: The circumference is greater than 60.

Possible Answers:

True

False

Correct answer:

True

Explanation:

The circumference of a circle is its diameter multiplied by $\pi$ , so, since the diameter is 20, the circumference is $20 \pi$ . Also,

$\pi > 3$ ,

so, multiplying both sides by 20 by the Multiplication Property of Inequality,

$20 \pi >20 \cdot 3$

and

$20 \pi >60$ .

The circumference is indeed greater than 60.

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Example Question #1 : How To Find Circumference

Ashley has a square room in her apartment that measures 81 square feet. What is the circumference of the largest circular area rug that she can fit in the space?

Possible Answers:

$10\pi$

$8\pi$

$81\pi$

$18\pi$

$9\pi$

Correct answer:

$9\pi$

Explanation:

In order to solve this question, first calculate the length of each side of the room.

A=s^2

81=s^2

s=9

The length of each side of the room is also equal to the length of the diameter of the largest circular rug that can fit in the room. Since $C=\pi d$ , the circumference is simply

$C=9\pi$

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Example Question #1 : How To Find The Length Of The Diameter

Give the diameter of a circle whose circumference is $36 \pi$ .

Possible Answers:

Correct answer:

Explanation:

$C = \pi d$

$36 \pi = \pi d$

d = 36

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Example Question #2 : Diameter

The perimeter of a circle is 36 π. What is the diameter of the circle?

Possible Answers:

Correct answer:

Explanation:

The perimeter of a circle = 2 πr = πd

Therefore d = 36

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Example Question #1 : How To Find The Length Of The Diameter

Two circles have only one point in common. Both circles have radii of . If point is on the first circle and point is on the second circle, what is longest possible distance of line ?

Possible Answers:

Correct answer:

Explanation:

The first step is to sketch two circles touching at a single point. In order to maximize the length of , the point and the point would need to be on opposite ends, as shown in the diagram. If the radius of a circle is , then the diameter would be 2r = 2(6) = 12 . Therefore, the length of would be 2d = 2(12) = 24 .

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Example Question #1 : How To Find The Length Of The Diameter

What is the name of the segment in green?

Possible Answers:

Radius

Ray

Diagonal

Chord

Diameter

Correct answer:

Diameter

Explanation:

The diameter is the maximum distance between two points on a circle's perimeter. The diameter passes through the circle's center.

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Example Question #2 : How To Find The Length Of The Diameter

The area of a circle is $9\pi \; in^{2}$ . What is its diameter?

Possible Answers:

$3\; in$

$6\; in$

$12\; in$

$9\; in$

$15\; in$

Correct answer:

$6\; in$

Explanation:

First solve for the radius:

$A=\pi r^{2} = 9\pi$

$r = 3 \; in$

Note that d = 2r , where is the radius and is the diameter.

Therefore, $d = 6\; in$ .

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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #106 : How To Find Circumference

Example Question #302 : Circles

Example Question #301 : Circles

Example Question #301 : Radius

Example Question #1 : How To Find Circumference

Example Question #1 : How To Find The Length Of The Diameter

Example Question #2 : Diameter

Example Question #1 : How To Find The Length Of The Diameter

Example Question #1 : How To Find The Length Of The Diameter

Example Question #2 : How To Find The Length Of The Diameter

All Basic Geometry Resources

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