GMAT Math : Calculating the area of a circle

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Example Question #21 : Radius

A circle has a radius of $7\:cm$ . Calculate the area of the circle.

Possible Answers:

$7\pi\:cm^2$

$49\pi\:cm^2$

$3.5\pi\:cm^2$

$14\pi\:cm^2$

$56\pi\:cm^2$

Correct answer:

$49\pi\:cm^2$

Explanation:

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

$A=\pi r^2=\pi (7\:cm)^2=49\pi\:cm^2$

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Example Question #22 : Calculating The Area Of A Circle

What is the area of a circle with a diameter of 18cm ?

Possible Answers:

$36\pi cm^2$

$324\pi cm^2$

$54\pi cm^2$

$90\pi cm^2$

$81\pi cm^2$

Correct answer:

$81\pi cm^2$

Explanation:

The area of a circle is defined by $A=\pi r^{2}$ , where is the radius of the circle. We are provided with the diameter of the circle, which is twice the length of .

If d=18cm , then $r=\frac{d}{2}=\frac{18cm}{2}=9cm$

Then, solving for :

$A=\pi r^{2}$

$A=\pi (9cm)^{2}$

$A=81\pi cm^2$

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Example Question #23 : Calculating The Area Of A Circle

A circle on the coordinate plane is defined by the equation $x^{2}+y^{2}=25$ . What is the area of the circle?

Possible Answers:

Not enough information provided.

$25\pi$

$50\pi$

$60\pi$

$5\pi$

Correct answer:

$25\pi$

Explanation:

The equation of a circle centered at the origin of the coordinate plane is $x^{2}+y^{2}=r^{2}$ , where is the radius of the circle.

The area of the circle, in turn, is defined by the equation $A=\pi r^{2}$ .

Since we are provided with the equation $x^{2}+y^{2}=25$ , we can deduce that $r^{2}=25$ and that $A=25\pi$ .

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Example Question #24 : Calculating The Area Of A Circle

What is the area of a circle with a diameter of 20cm ?

Possible Answers:

$40\pi cm^2$

$100\pi cm^2$

$20\pi cm^2$

Not enough information provided.

$400\pi cm^2$

Correct answer:

$100\pi cm^2$

Explanation:

The area of a circle is defined by $A=\pi r^{2}$ , where is the radius of the circle. We are provided with the diameter of the circle, which is twice the length of .

If d=20cm , then $r=\frac{d}{2}=\frac{20cm}{2}=10cm$

Therefore:

$A=\pi r^{2}$

$A=\pi (10cm)^{2}$

$A=100\pi cm^2$

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Example Question #25 : Calculating The Area Of A Circle

4c 43438 lg A square is inscribed in a circle of r=5 .

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

Possible Answers:

$\textup{Cannot be determined}$

$25\pi$

$25\pi - 25$

$25\pi - 50$

Correct answer:

$25\pi - 50$

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 $5\sqrt{2}$ .

Now we can find the square's area:

$A_{s} = (5\sqrt{2})^{2} = 50$

and the circle's area:

$A_{c} = \pi(5)^{2} = 25\pi$

Finally we subtract the square's area from the circle's area:

$A_{c} - A_{s} = 25\pi - 50$

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Example Question #291 : Problem Solving Questions

An engineer is designing a circular hatch for a submarine. If the hatch must have a circumference of 4.56m , what will its area be?

Possible Answers:

3.14m^2

1.65m^2

3.45m^2

.73m^2

Correct answer:

1.65m^2

Explanation:

An engineer is designing a circular hatch for a submarine. If the hatch must have a circumference of 4.56m , what will its area be?

To find area, we will need the radius. We can find the radius using the following formula:

$Circumference=2 \pi r$

So, plug in and solve for r

$4.56m=2 \pi r$

$r\approx.73m$

Next, use the area formula to find the area:

$A_{circle}=\pi r^2$

$A_{circle}=\pi (.73m)^2\approx 1.65m^2$

So we have our answer!

1.65m^2

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Example Question #27 : Calculating The Area Of A Circle

and are the area and the diameter of the same circle.

$A = \frac{1}{L}$

$d = t^{2}$ .

Which of the following is a true statement?

Possible Answers:

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 .

Correct answer:

varies inversely as the fourth power of .

Explanation:

The area and the diameter of a circle are related by the formula

$A = \frac{1}{4} \pi d^{2}$

Substituting:

$\frac{1}{L} = \frac{1}{4} \pi (t^{2}) ^{2}$

$\frac{1}{L} = \frac{\pi t^{4} }{4}$

$L= \frac{4}{\pi t^{4} }$

If $K = \frac{4}{\pi}$ , then

$L = \frac{K}{t^{4}}$ ,

and varies inversely as the fourth power of .

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Example Question #28 : Calculating The Area Of A Circle

A circle has radius $\pi ^{t}$ . Give its area.

Possible Answers:

$\pi ^{2t+1}$

$2 \pi ^{2t}$

$\pi ^{t+2}$

$\pi ^{t+1}$

$2 \pi ^{t+1}$

Correct answer:

$\pi ^{2t+1}$

Explanation:

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

$A = \pi r^{2}$

Set $r= \pi ^{t}$ :

$A = \pi \cdot ( \pi ^{t}) ^{2}$

$A = \pi^{1} \cdot \pi ^{2t}$

$A = \pi ^{2t+1}$

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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?

Possible Answers:

$A\approx 37.70 in^2$

$A\approx0.95 in^2$

$A\approx 2.86 in^2$

$A\approx 11.45 in^2$

Correct answer:

$A\approx 2.86 in^2$

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:

$Circ=\pi 2 r$

Use this to find "r" which we will use to find the area:

$6=2 \pi r$

$r=\frac{3}{\pi}$

Next, find area using the following:

$A=\pi r^2$

$A=\pi (\frac{3}{\pi})^2$

$A\approx 2.86 in^2$

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GMAT Math : Calculating the area of a circle

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #21 : Radius

Example Question #22 : Calculating The Area Of A Circle

Example Question #23 : Calculating The Area Of A Circle

Example Question #24 : Calculating The Area Of A Circle

Example Question #25 : Calculating The Area Of A Circle

Example Question #291 : Problem Solving Questions

Example Question #27 : Calculating The Area Of A Circle

Example Question #28 : Calculating The Area Of A Circle

Example Question #29 : Calculating The Area Of A Circle

All GMAT Math Resources

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