All GMAT Math Resources
Example Questions
Example Question #21 : Calculating The Area Of A Circle
What is the area of a circle with a diameter of ?
Not enough information provided.
The area of a circle is defined by , where is the radius of the circle. We are provided with the diameter of the circle, which is twice the length of .
If , then
Therefore:
Example Question #51 : Geometry
A square is inscribed in a circle of .
What is the area of the region inside the circle but not inside the square?
Our first step will be to draw two radii, from the circle's center to two adjacent vertexes of the square, forming a triangle, the third side of which is the edge of the square. Because these radii bisect the square's right angles, we can determine that the triangle we drew is a 45˚ - 45˚ - 90˚ right triangle. Because of the rules governing those isoceles right triangles, we can then determine that, because the two legs of the triangle are 5 (radius = 5), the hypotenuse (the square's side) must equal .
Now we can find the square's area:
and the circle's area:
Finally we subtract the square's area from the circle's area:
Example Question #291 : Problem Solving Questions
An engineer is designing a circular hatch for a submarine. If the hatch must have a circumference of , what will its area be?
An engineer is designing a circular hatch for a submarine. If the hatch must have a circumference of , what will its area be?
To find area, we will need the radius. We can find the radius using the following formula:
So, plug in and solve for r
Next, use the area formula to find the area:
So we have our answer!
Example Question #27 : Calculating The Area Of A Circle
and are the area and the diameter of the same circle.
.
Which of the following is a true statement?
varies directly as the square of .
varies directly as the fourth power of .
varies directly as the square root of .
varies inversely as the fourth power of .
varies inversely as the square of .
varies inversely as the fourth power of .
The area and the diameter of a circle are related by the formula
Substituting:
If , then
,
and varies inversely as the fourth power of .
Example Question #21 : Calculating The Area Of A Circle
A circle has radius . Give its area.
The area of a circle is found using the following formula:
Set :
Example Question #26 : Calculating The Area Of A Circle
If the pitcher plant Sarracenia purpurea has a circular opening with a circumference of 6 inches, what is the area of the opening?
If the pitcher plant Sarracenia purpurea has a circular opening with a circumference of 6 inches, what is the area of the opening?
We need to work backward from circumference to find area.
Circumference can be found as follows:
Use this to find "r" which we will use to find the area:
Next, find area using the following:
Example Question #1 : Calculating The Length Of A Radius
A square and a circle have the same area. What is the ratio of the length of one side of the square to the radius of the circle?
Let be the sidelength of the square is the square and be the radius of the circle. Then since the areas of the circle and the square are equal, we can set up this equation:
We find the ratio of to - that is, - as follows:
The correct ratio is .
Example Question #1 : Calculating The Length Of A Radius
The radius of Circle A is three times the radius of Circle B, which is, in turn, equal to the diameter of Circle C. The sum of their circumferences is . What is the radius of Circle C?
Let be the radius of circle C. Then Circle B has radius equal to twice this, or , and Circle A has radius equal to three times that, or . The circumference of a circle is equal to times the radius, so the circumferences of the three circles are:
A:
B:
C:
These circumferences add up to , so set up and solve the equation:
Example Question #2 : Calculating The Length Of A Radius
The points and form a line which passes through the center of circle Q. Both points are on circle Q.
To the nearest hundreth, what is the length of the radius of circle Q?
To begin this problem, we need to recognize that the distance between points L and K is our diameter. Segment LK passes from one point on circle Q through the center, to another point on circle Q. Sounds like a diameter to me! Use distance formula to find the length of LK.
Plug in our points and simplify:
Now, don't be fooled into choosing 13.15. That is our diameter, so our radius will be half of 13.15, or 6.575. This rounds to 6.58
Example Question #3 : Calculating The Length Of A Radius
If the trunk of a particular tree is feet around at chest height, what is the radius of the tree at the same height?
A close reading of the question reveals that we are given the circumference and asked to find the radius.
Circumference formula:
So,
So 17 feet