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Basic Geometry : Diameter

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Example Questions

Example Question #1 : 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 #1 : 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 #2 : 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 #3 : Diameter

What is the name of the segment in green?

Possible Answers:

Chord

Diameter

Diagonal

Radius

Ray

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 : Diameter

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

Possible Answers:

$3\; in$

$12\; in$

$9\; in$

$15\; in$

$6\; in$

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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Example Question #3 : Diameter

A circle has an area of $60\pi$ cm^2 . What is the circle's diameter?

Possible Answers:

$2\sqrt{15}\pi$

$4\sqrt{15}$

$2\sqrt{15}$

Correct answer:

$4\sqrt{15}$

Explanation:

The area of a circle is given by the equation $A = \pi r^2$ , where is the area and is the radius. Use the given area in this equation and solve for to find the circle's radius.

$60\pi = \pi r^2$

$\frac{(60\pi)}{\pi} = \frac{(\pi r^2)}{\pi}$

60 = r^2

$\sqrt{60} = \sqrt{r^2}$

$r = \sqrt{60} = 2\sqrt{15}$

To find the circle's diameter, multiply its radius by .

$2\sqrt{15} * 2 = 4\sqrt{15}$

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Example Question #1 : Diameter

A circle has a radius of 7 inches. What is the diameter of the circle?

Possible Answers:

inches

Correct answer:

inches

Explanation:

The diameter of a circle can be written as d=2r , where is the radius and is the diameter.

(7) 2 = 14

Therefore the diameter of the circle is 14 inches.

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Example Question #5 : Diameter

Two legs of a right triangle measure 3 and 4, respectively. What is the area of the circle that circumscribes the triangle?

Possible Answers:

$5\pi$

$25\pi$

$6.25\pi$

$12.5\pi$

$6\pi$

Correct answer:

$6.25\pi$

Explanation:

For the circle to contain all 3 vertices, the hypotenuse must be the diameter of the circle. The hypotenuse, and therefore the diameter, is 5, since this must be a 3-4-5 right triangle.

The equation for the area of a circle is A = πr².

$A=\pi (5/2)^2=6.25\pi$

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Example Question #7 : How To Find The Length Of The Diameter

If the area of a circle is $9\pi$ , what is its diameter?

Possible Answers:

Correct answer:

Explanation:

Before we can find the diameter of this circle, we need to find its radius. We need to use the formula for the area of a cirlce:

$A=\pi r^2$

Given that the area is $9\pi$ , we can find the radius

$9\pi=\pi r^2$

cancel the pi and then square root it to find 'r'.

9=r^2

3=r

Now that the radius is found, we can find the diamater by multiplying it by 2.

D=2r=2(3)=6

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Example Question #3 : How To Find The Length Of The Diameter

Find the diameter of a circle that has an area of $144\pi$ .

Possible Answers:

$24\pi$

144

Correct answer:

Explanation:

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$

Next, plug in the information given by the question.

$144\pi=\pi\times\text{radius}^2$

From this, we can see that we can solve for the radius.

$\text{radius}^2=144$

$\text{radius}=\sqrt{144}=12$

Now recall the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Plug in the value of the radius to find the diameter.

$\text{diameter}=2\times 12 = 24$

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Basic Geometry : Diameter

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #1 : Diameter

Example Question #1 : Diameter

Example Question #2 : Diameter

Example Question #3 : Diameter

Example Question #2 : Diameter

Example Question #3 : Diameter

Example Question #1 : Diameter

Example Question #5 : Diameter

Example Question #7 : How To Find The Length Of The Diameter

Example Question #3 : How To Find The Length Of The Diameter

All Basic Geometry Resources

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