# GMAT Math : Calculating the area of a circle

## Example Questions

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### Example Question #21 : Calculating The Area Of A Circle

A circle has a radius of . Calculate the area of the circle.

Explanation:

Using the formula for the area of a circle, we can plug in the given value for its radius and calculate our solution:

### Example Question #22 : Calculating The Area Of A Circle

What is the area of a circle with a diameter of ?

Explanation:

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

Then, solving for :

### Example Question #23 : Calculating The Area Of A Circle

A circle on the coordinate plane is defined by the equation . What is the area of the circle?

Not enough information provided.

Explanation:

The equation of a circle centered at the origin of the coordinate plane is , where  is the radius of the circle.

The area  of the circle, in turn, is defined by the equation .

Since we are provided with the equation , we can deduce that  and that .

### Example Question #24 : Calculating The Area Of A Circle

What is the area of a circle with a diameter of ?

Not enough information provided.

Explanation:

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 #25 : Calculating The Area Of A Circle

A square is inscribed in a circle of

What is the area of the region inside the circle but not inside the square?

Explanation:

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 #26 : Calculating The Area Of A Circle

An engineer is designing a circular hatch for a submarine. If the hatch must have a circumference of , what will its area be?

Explanation:

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:

### 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 inversely as the square of .

varies inversely as the fourth power of .

varies directly as the fourth power of .

varies directly as the square root of .

varies directly as the square of .

varies inversely as the fourth power of .

Explanation:

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 #28 : Calculating The Area Of A Circle

A circle has radius . Give its area.

Explanation:

The area of a circle is found using the following formula:

Set :

### Example Question #29 : 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?

Explanation:

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:

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