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GED Math : Area of a Circle

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Example Question #157 : Geometry And Graphs

Find the area of a circle given that it's circumference is $20\pi$ .

Possible Answers:

$1000\pi$

$20\pi$

$100\pi$

$5\pi$

$10\pi$

Correct answer:

$100\pi$

Explanation:

In order to find the area of a circle, we must know the formula that will give us the appropriate answer. The area of a circle is $A=\pi r^2$ , where r is the radius.

However, the problem doesn't give us radius. The only value provided is the circumference. The formula for circumference is $C = \pi d$ , where d is diameter. So what is the relationship between these two formulas? Since the diameter of a circle is twice the radius, we can see that the relationship helps us find r to solve for the area.

The circumference equation can be rewritten as $C= \pi \cdot 2r$

In order to solve for the radius, we must substitute in the circumference value provided. This will allow us to solve for r.

$20\pi = \pi \cdot 2r$

$\frac{20\pi}{2\pi}=r$

r=10

Now that we know that value of r, the area can be solved for.

$A = \pi (10^2)$

$A = 100\pi$

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Example Question #158 : Geometry And Graphs

Find the area of a circle given that it's circumference is $14\pi$ .

Possible Answers:

$2\pi$

$7\pi$

$196\pi$

$14\pi$

$49\pi$

Correct answer:

$49\pi$

Explanation:

In order to find the area of a circle, we must know the formula that will give us the appropriate answer. The area of a circle is $A=\pi r^2$ , where r is the radius.

The circumference equation can be rewritten as $C= \pi \cdot 2r$

In order to solve for the radius, we must substitute in the circumference value provided. This will allow us to solve for r.

$14\pi = \pi \cdot 2r$

$\frac{14\pi}{2\pi}=r$

r=7

Now that we know that value of r, the area can be solved for.

$A = \pi (7^2)$

$A = 49\pi$

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Example Question #159 : Geometry And Graphs

What is the area of a circle if it has a circumference of 37.68 ?

Possible Answers:

$27\pi$

$4\pi$

$36\pi$

$37\pi$

$12\pi$

Correct answer:

$36\pi$

Explanation:

In order to find the area of a circle, we must know the formula that will give us the appropriate answer. The area of a circle is $A=\pi r^2$ , where r is the radius.

The circumference equation can be rewritten as $C= \pi \cdot 2r$

In order to solve for the radius, we must substitute in the circumference value provided. This will allow us to solve for r.

$37.68 = \pi \cdot 2r$

$\frac{37.68}{2\pi}=r$

r=6

Now that we know that value of r, the area can be solved for.

$A = \pi (6^2)$

$A = 36\pi$

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Example Question #152 : 2 Dimensional Geometry

Find the area of a circle, given that it's diameter is 13.

Possible Answers:

$7.5\pi$

$34.33\pi$

$13\pi$

$42.5\pi$

$56.25\pi$

Correct answer:

$56.25\pi$

Explanation:

In order to find the area of a circle, we must know the formula that will give us the appropriate answer. The area of a circle is $A=\pi r^2$ , where r is the radius.

However, the problem doesn't give us a value for the radius. The only value provided is the diameter. The formula for diameter is d=2r , where d is diameter and r is radius. Using this relationship will help us find r so we can solve for the area.

13=2r

$\frac{13}{2}=r$

r=7.5

Now that we know that value of r, the area can be solved for.

$A = \pi (7.5^2)$

$A = 56.25\pi$

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Example Question #1121 : Ged Math

What is the area of a circle if it has a diameter of ?

Possible Answers:

$144\pi$

$36\pi$

$24\pi$

$74\pi$

$12\pi$

Correct answer:

$144\pi$

Explanation:

In order to find the area of a circle, we must know the formula that will give us the appropriate answer. The area of a circle is $A=\pi r^2$ , where r is the radius.

24=2r

$\frac{24}{2}=r$

r=12

Now that we know that value of r, the area can be solved for.

$A = \pi (12^2)$

$A = 144\pi$

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Example Question #161 : Geometry And Graphs

Find the area of a circle that has a radius of meters.

Possible Answers:

$256\pi$ meters^2

$24\pi$ meters^2

$16\pi$ meters^2

$8\pi$ meters^2

$64\pi$ meters^2

Correct answer:

$256\pi$ meters^2

Explanation:

In order to find the area of a circle, we must know the formula that will give us the appropriate answer. The area of a circle is $A=\pi r^2$ , where r is the radius.

Since the problem provides the value of the radius, we just need to substitute in the value for r in order to solve for area

$A = \pi (16^2)$

$A = 256\pi$ meters^2

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Example Question #163 : Geometry And Graphs

The diameter of a circle is . Find the area.

Possible Answers:

$25\Pi$

$100\Pi$

$5\Pi$

$10\Pi$

Correct answer:

$25\Pi$

Explanation:

The formula for the area of a circle is

$area = \Pi r^2$

with standing for radius.

In this problem, however, you are given the diameter, not the radius. You therefore need to solve for the radius first. This is simple. The diameter is twice the length of the radius, so if the diameter is , the radius is . (10 / 2 = 5) .

Once you have the radius, you can plug it into the formula for the area of a circle, and solve.

$\Pi r^2 = \Pi (5)^2 = 25\Pi$

So, the area of the circle is $25\Pi$ .

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Example Question #164 : Geometry And Graphs

You and your friends are ordering pizza for your Friday night Mathathon. You decide to order three pizzas, each 16" in diameter. Find the area of each pizza to the nearest tenth.

Possible Answers:

A=401.1 in^2

A=603.2 in^2

A=201.1 in^2

A=804.2 in^2

Correct answer:

A=201.1 in^2

Explanation:

You and your friends are ordering pizza for your Friday night Mathathon. You decide to order three pizzas, each 16" in diameter. Find the area of each pizza to the nearest tenth.

First, let's convert our diameter to radius:

$r=\frac{d}{2}=\frac{16 in}{2}=8 in$

Next, use the following formula to solve for Area.

$A=\pi r^2= \pi (8in)^2=64 \pi in ^2 \approx 201.1 in^2$

So, our answer is:

A=201.1 in^2

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Example Question #165 : Geometry And Graphs

A $90 ^{\circ }$ arc of a circle has length $7 \pi$ . Which expression gives its area?

Possible Answers:

$196 \pi$

196

$98 \pi$

Correct answer:

$196 \pi$

Explanation:

A $90 ^{\circ }$ arc of the circle is one fourth of the circle, so the length of the arc is

$L = \frac{1}{4}C$ ,

where is its circumference.

Since $L = 7 \pi$ , substitute as follows:

$\frac{1}{4}C = 7 \pi$

Multiply both sides by 4:

$\frac{1}{4}C \cdot 4 = 7 \pi \cdot 4$

$C = 28 \pi$

The radius of a circle is its circumference divided by $2 \pi$ , so

$r= \frac{C}{2\pi}$

$r= \frac{28 \pi }{2\pi} = 14$

Substitute this for in the formula

$A = \pi r^{2}$

to get

$A = \pi \cdot 14^{2} = \pi \cdot 14 \cdot 14 = 196 \pi$ ,

the correct choice.

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Example Question #161 : Circles

Use 3.14 for pi and round your answer to the nearest hundredth.

Find the area of a circle with a diameter of 12cm.

Possible Answers:

$452.16cm^{2}$

$113.04cm^{2}$

452.16cm

$37.68cm^{2}$

113.04cm

Correct answer:

$113.04cm^{2}$

Explanation:

First we need to recall that the formula for area of a circle is

$Area=r^{2}\cdot \pi$

Where is radius and $\pi$ is 3.14

The circe we are working with has a diameter of 12. The diameter is twice the length of the radius, so to find the radius we cut it in half, and we get 6cm.

Now we can plug our radius and pi into our equation and solve for the area

$Area=(6cm)^{2}\cdot3.14$

Following order of operations, first we need to address the exponent. Any number to the second power (squared) is that number times itself one time (in this case it is 6x6)

$Area=36cm^{2}\cdot3.14$

Next we multiply

$Area=113.04cm^{2}$

Since we multiplied two terms whose units are in cm, our answer is in centimeters squared.

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GED Math : Area of a Circle

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #157 : Geometry And Graphs

Example Question #158 : Geometry And Graphs

Example Question #159 : Geometry And Graphs

Example Question #152 : 2 Dimensional Geometry

Example Question #1121 : Ged Math

Example Question #161 : Geometry And Graphs

Example Question #163 : Geometry And Graphs

Example Question #164 : Geometry And Graphs

Example Question #165 : Geometry And Graphs

Example Question #161 : Circles

All GED Math Resources

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