Basic Geometry : How to find the length of the diameter

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

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

Give the diameter of a circle whose circumference is .

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : Diameter

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

Possible Answers:

18

36

3

72

6

Correct answer:

36

Explanation:

The perimeter of a circle = 2 πr = πd

Therefore d = 36

Example Question #2 : 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:

24

6

18

20

12

Correct answer:

24

Explanation:

Circle

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 . Therefore, the length of would be .

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

Circle_line_identity

What is the name of the segment in green?

Possible Answers:

Ray

Diagonal

Chord

Diameter

Radius

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.

Example Question #4 : How To Find The Length Of The Diameter

The area of a circle is .  What is its diameter?

Possible Answers:

Correct answer:

Explanation:

First solve for the radius:

 

  

Note that , where is the radius and is the diameter. 

Therefore, .

Example Question #5 : How To Find The Length Of The Diameter

A circle has an area of . What is the circle's diameter?

Possible Answers:

 

 

 

 

Correct answer:

 

 

Explanation:

The area of a circle is given by the equation , where  is the area and  is the radius. Use the given area in this equation and solve for  to find the circle's radius.

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

Example Question #6 : How To Find The Length Of The Diameter

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

Possible Answers:

 inches

 inches

 inches

inches

 inches

Correct answer:

inches

Explanation:

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

Therefore the diameter of the circle is 14 inches.

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

Correct answer:

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.

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

If the area of a circle is , 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:

Given that the area is , we can find the radius

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

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

Example Question #8 : How To Find The Length Of The Diameter

Find the diameter of a circle that has an area of .

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a circle:

Next, plug in the information given by the question.

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

Now recall the relationship between the radius and the diameter.

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

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