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Example Questions
Example Question #1 : 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?
cm
cm
cm
cm
cm
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 #21 : 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?
The relationship of the quantities cannot be determined.
Quantity B is larger.
Quantity A is larger.
Both quantities are equal.
Quantity B is larger.
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 #21 : 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?
Quantity B is larger.
Quantity A is larger.
The relationship between the quantities cannot be determined.
The two quantities are equal.
Quantity B is larger.
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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