GRE Math : How to find the length of the diameter

Study concepts, example questions & explanations for GRE Math

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Example Questions

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

The formula to find the radius of the largest circle that can fit in an equilateral triangle is , where  is the length of any one side of the triange.  

What is the largest diameter of a circle that can fit inside an equilateral triangle with a perimeter of  cm?

Possible Answers:

 cm

 cm

 cm

 cm

Correct answer:

 cm

Explanation:

The diameter is

To solve for the largest diameter multiply each side by 2.  

The resulting formula for diamenter is

 .  

Substitute in 5  for S and solve. Diameter =  = 2.89 cm 

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

Quantity A: The diameter of a circle with area of 

Quantity B: The diameter of a circle with circumference of 

Which of the following is true?

Possible Answers:

The relationship of the quantities cannot be determined.

Quantity A is larger.

Both quantities are equal.

Quantity B is larger.

Correct answer:

Quantity B is larger.

Explanation:

Consider each quantity separately.

 

Quantity A

Recall that the area of a circle is defined as:

We know that the area is . Therefore,

Divide both sides by :

Therefore, . Since , we know:

 

Quantity B

This is very easy. Recall that:

Therefore, if . Therefore, Quantity B is larger.

Example Question #25 : Plane Geometry

Quantity A: The diameter of a circle with area of 

Quantity B: The diameter of a circle with circumference of 

Which of the following is true?

Possible Answers:

Quantity A is larger.

The relationship between the quantities cannot be determined.

The two quantities are equal. 

Quantity B is larger.

Correct answer:

Quantity B is larger.

Explanation:

Consider each quantity separately.

 

Quantity A

Recall that the area of a circle is defined as:

We know that the area is . Therefore,

Divide both sides by :

Therefore, .  Since , we know:

 

Quantity B

This is very easy.  Recall that:

Therefore, if .  

 

Now, since your calculator will not have a square root button on it, we need to estimate for Quantity A. We know that  is . Therefore, .  This means that . Therefore, Quantity B is larger.

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