All ISEE Upper Level Math Resources
Example Questions
Example Question #1 : Radius
What is the radius of a circle with circumference equal to ?
The circumference of a circle can be found using the following equation:
Example Question #1 : How To Find The Length Of A Radius
What is the value of the radius of a circle if the area is equal to ?
The equation for finding the area of a circle is .
Therefore, the equation for finding the value of the radius in the circle with an area of is:
Example Question #165 : Plane Geometry
What is the radius of a circle with a circumference of ?
The circumference of a circle can be found using the following equation:
We plug in the circumference given, into and use algebraic operations to solve for .
Example Question #4 : How To Find The Length Of A Radius
Refer to the above diagram. has length . Give the radius of the circle.
Inscribed , which measures , intercepts a minor arc with twice its measure. That arc is , which consequently has measure
.
The corresponding major arc, , has as its measure
, and is
of the circle.
If we let be the circumference and be the radius, then has length
.
This is equal to , so we can solve for in the equation
The radius of the circle is 50.
Example Question #1 : How To Find The Length Of A Radius
A circle has a circumference of . What is the radius of the circle?
Not enough information to determine.
A circle has a circumference of . What is the radius of the circle?
Begin with the formula for circumference of a circle:
Now, plug in our known and work backwards:
Divide both sides by two pi to get:
Example Question #6 : How To Find The Length Of A Radius
You are exploring the woods near your house, when you come across an impact crater. It is perfectly circular, and you estimate its area to be .
What is the radius of the crater?
Cannot be determined from the information provided
You are exploring the woods near your house, when you come across an impact crater. It is perfectly circular, and you estimate its area to be .
What is the radius of the crater?
To solve this, we need to recall the formula for the area of a circle.
Now, we know A, so we just need to plug in and solve for r!
Begin by dividing out the pi
Then, square root both sides.
So our answer is 13m.