All GMAT Math Resources
Example Questions
Example Question #15 : Calculating The Length Of A Radius
If a monster truck's wheels have circumference of , what is the distance from the ground to the center of the wheel?
If a monster truck's wheels have circumference of , what is the distance from the ground to the center of the wheel?
This question is asking us to find the radius of a circle. the distance from the outside of the circle to the center is the radius. We are given the circumference, so use the following formula:
Then, plug in what we know and solve for r
Example Question #311 : Gmat Quantitative Reasoning
Two circles in the same plane have the same center. The smaller circle has radius 10; the area of the region between the circles is . What is the radius of the larger circle?
The area of a circle with radius is .
Let be the radius of the larger circle. Its area is . The area of the smaller circle is . Since the area of the region between the circles is , and is the difference of these areas, we have
The smaller circle has radius .
Example Question #1 : Calculating Circumference
A circle on the coordinate plane has equation
Which of the following represents its circumference?
The equation of a circle centered at the origin is
where is the radius of the circle.
In this equation, , so ; this simplifies to
The circumference of a circle is , so substitute :
Example Question #1 : Calculating Circumference
A circle on the coordinate plane has equation
What is its circumference?
The standard form of the area of a circle with radius and center is
Once we get the equation in standard form, we can find radius , and multiply it by to get the circumference.
Complete the squares:
so can be rewritten as follows:
,
so
And
Example Question #311 : Problem Solving Questions
On average, Stephanie walks feet every seconds. If Stephanie walks at her usual pace, how long will it take her to walk around a circular track with a radius of feet, in seconds?
seconds
seconds
seconds
seconds
None of the other answers are correct.
seconds
The length of the track equals the circumference of the circle.
Therefore, .
Example Question #72 : Circles
A circle on the coordinate plane has equation .
What is its circumference?
The equation of a circle centered at the origin is
,
where is the radius of the circle.
In the equation given in the question stem, , so .
The circumference of a circle is , so substitute :
Example Question #2 : Calculating Circumference
Let be concentric circles. Circle has a radius of , and the shortest distance from the edge of circle to the edge of circle is . What is the circumference of circle ?
Since are concentric circles, they share a common center, like sections of a bulls-eye target. Since the radius of is less than half the distance from the edge of to the edge of , we must have circle is inside of circle . (It's helpful to draw a picture to see what's going on!)
Now we can find the radius of by adding and , which is And the equation for finding circumfrence is . Plugging in for gives .
Example Question #2 : Calculating Circumference
Consider the Circle :
(Figure not drawn to scale.)
Suppose Circle represents a circular pen for Frank's mules. How many meters of fencing does Frank need to build this pen?
We need to figure out the length of fencing needed to surround a circular enclosure, or in other words, the circumference of the circle.
Circumference equation:
Where is our radius, which is in this case. Plug it in and simplify:
And we have our answer!
Example Question #2 : Calculating Circumference
If the radius of a circle is , what is its circumference?
Using the formula for the circumference of a circle, we can plug in the given value for the radius and calculate our solution:
Example Question #8 : Calculating Circumference
Megan, a civil engineer, is designing a roundabout for the city of Madison. She knows that the distance from the edge of the roundabout to the center must be 25 meters. Help Megan find the circumference of the roundabout.
Megan, a civil engineer, is designing a roundabout for the city of Madison. She knows that the distance from the edge of the roundabout to the center must be 25 meters. Help Megan find the circumference of the roundabout.
We are asked to find circumference. In order to do so, look at the following formula:
Where r is our radius and C is our circumference.
We are indirectly told that our radius is 25 meters, plug it in to get our answer: