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GED Math : Geometry and Graphs

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4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #151 : Geometry And Graphs

Determine the area of a circle with a radius of .

Possible Answers:

$16\pi ^2x^2$

$16\pi x^2$

64x^2

$64\pi x^2$

$64\pi ^2x^2$

Correct answer:

$64\pi x^2$

Explanation:

Write the formula for the area of a circle.

$A =\pi r^2$

Substitute the known radius.

$A =\pi (8x)^2=\pi (8x)(8x)$

The answer is: $64\pi x^2$

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Example Question #151 : Circles

You have a giant gong that has a diameter of 1.5 m . Find the area of the gong.

Possible Answers:

7.07 m^2

1.77 m^2

0.5625 m^2

2.25m^2

Correct answer:

1.77 m^2

Explanation:

You have a giant gong that has a diameter of 1.5 m . Find the area of the gong.

To relate radius and diameter, use the following formula:

d=2r

So, to find our radius from our diameter, divide by 2:

$1.5m=2r\rightarrow\frac{1.5m}{2}=r\rightarrow r= 0.75m$

Next, recall the following formula for area:

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

So, plug in our radius and solve.

$A_{circle}=\pi (0.75m)^2=.5625 \pi m^2=1.77 m^2$

Making our answer:

1.77 m^2

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Example Question #151 : Geometry And Graphs

If the circumference of a circle is 50.24 in , what is the area of the circle in square inches? Use $\pi=3.14$ .

Possible Answers:

224.08

182.36

194.88

200.96

Correct answer:

200.96

Explanation:

Recall how to find the circumference of a circle.

$\text{Circumference}=2\pi r$ , where is the radius.

Plug in the given circumference and solve for the radius.

$50.24=2\pi r$

r=8

Next, recall how to find the area of a circle.

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

Plug in the given radius to find the area.

$\text{Area}=(3.14)(8)^2=200.96$

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Example Question #154 : Geometry And Graphs

While doing your homework, you become distracted by the 3 holes on the margin of your paper. You estimate that the holes have a diameter of 2.5 cm. What is the area of the circles?

Possible Answers:

12.65 cm^2

19.63cm^2

4.91 cm^2

6.25 cm^2

Correct answer:

4.91 cm^2

Explanation:

While doing your homework, you become distracted by the 3 holes on the margin of your paper. You estimate that the holes have a diameter of 2.5 cm. What is the area of the circles?

To find the area of a circle, we first need to find our radius:

$r=\frac{d}{2}=\frac{2.5cm}{2}=1.25cm$

Next, use the following formula to find the area:

$A=\pi r^2=\pi (1.25cm)^2=\pi 1.5625cm^2\approx4.91cm^2$

So our answer is 4.91 cm^2

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Example Question #151 : Circles

You have a circular desk which you study at. If the desk has a radius of 2.5 ft, what is its area?

Possible Answers:

9.36 ft^2

6.25 ft^2

16.23 ft^2

19.63 ft^2

Correct answer:

19.63 ft^2

Explanation:

You have a circular desk which you study at. If the desk has a radius of 2.5 ft, what is its area?

Find the area of a circle with the following formula:

$A=\pi r ^2$

We know the radius is 2.5 ft, so plug and solve.

$A=\pi (2.5ft)^2=6.25ft^2 \pi\approx 19.63 ft^2$

So our answer is

19.63 ft^2

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Example Question #156 : Geometry And Graphs

Give the area of a circle with circumference $22 \pi$ .

Possible Answers:

$162 \pi$

$81 \pi$

$242 \pi$

$121 \pi$

Correct answer:

$121 \pi$

Explanation:

The radius of a circle can be determined by dividing its circumference by $2 \pi$ :

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

Set $C = 22\pi$ and evaluate :

$r = \frac{22 \pi}{2 \pi } = 11$

Now substitute 11 for in the area formula for a circle:

$A = \pi r^{2}$

$A = \pi \cdot 11^{2 }$

$A = 121 \pi$ square untis.

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Example Question #152 : Geometry And Graphs

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

Possible Answers:

$10\pi$

$20\pi$

$100\pi$

$5\pi$

$1000\pi$

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 #153 : Geometry And Graphs

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

Possible Answers:

$196\pi$

$7\pi$

$49\pi$

$2\pi$

$14\pi$

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 #154 : Geometry And Graphs

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

Possible Answers:

$12\pi$

$27\pi$

$37\pi$

$36\pi$

$4\pi$

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 #155 : Geometry And Graphs

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

Possible Answers:

$7.5\pi$

$42.5\pi$

$34.33\pi$

$56.25\pi$

$13\pi$

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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GED Math : Geometry and Graphs

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #151 : Geometry And Graphs

Example Question #151 : Circles

Example Question #151 : Geometry And Graphs

Example Question #154 : Geometry And Graphs

Example Question #151 : Circles

Example Question #156 : Geometry And Graphs

Example Question #152 : Geometry And Graphs

Example Question #153 : Geometry And Graphs

Example Question #154 : Geometry And Graphs

Example Question #155 : Geometry And Graphs

All GED Math Resources

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