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GED Math : Circles

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Example Questions

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Example Question #21 : Circles

Find the diameter if the radius is $\sqrt5$ .

Possible Answers:

$5\sqrt2$

$\sqrt{10}$

$2\sqrt5$

Correct answer:

$2\sqrt5$

Explanation:

The diameter is double the radius.

d=2r

Multiply the radical by two.

$d=2r = 2\cdot \sqrt5$

Do not multiply the coefficient into the radical.

The answer is: $2\sqrt5$

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Example Question #21 : Circles

Determine the diameter if the radius is 6x-9 .

Possible Answers:

36x-81

12x-9

12x-18

36x-9

12x-81

Correct answer:

12x-18

Explanation:

The diameter is double the radius.

D=2r

Substitute the radius into the formula.

D=2(6x-9) = 12x-18

The answer is: 12x-18

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Example Question #23 : Geometry And Graphs

A circle is circumscribed in a square as shown by the figure below.

If the area of the square is 144in^2 , what is the area of the circle in square inches? Use $\pi=3.14$ .

Possible Answers:

128.97

128.28

113.04

106.34

Correct answer:

113.04

Explanation:

Start by finding the length of a side of the square from the area.

$\text{Area}=\text{side}^2$

$\text{side}=\sqrt{\text{Area}}$

Plug in the area to find the length of the side.

$\text{side}=\sqrt{144}=12$

Now, notice that the diameter of the circle is the same as the length of a side of the square.

Thus, the diameter of the circle is , which means the radius is . Recall how to find the area of a circle:

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

$\text{Area}=\pi(6)^2=36\pi=113.04$

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Example Question #22 : Circles

Determine the diameter with a radius of $8\sqrt2$ .

Possible Answers:

$4\sqrt2$

$64\sqrt{2}$

$16\sqrt2$

Correct answer:

$16\sqrt2$

Explanation:

The diameter is double the radius.

d=2r

Substitute the radius.

$d=2(8\sqrt2) = 16\sqrt2$

The answer is: $16\sqrt2$

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Example Question #21 : Geometry And Graphs

Determine the radius if the diameter of a circle is: $\frac{3+\sqrt2}{3}$

Possible Answers:

$1+\sqrt2$

$1+\frac{\sqrt2}{2}$

$\frac{3+\sqrt2}{6}$

$1+\frac{\sqrt2}{4}$

$\frac{1}{2}+\frac{\sqrt2}{2}$

Correct answer:

$\frac{3+\sqrt2}{6}$

Explanation:

The radius is half the diameter.

Multiply the diameter by one-half.

$(\frac{3+\sqrt2}{3} )\cdot \frac{1}{2} = \frac{3+\sqrt2}{6}$

The answer is: $\frac{3+\sqrt2}{6}$

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Example Question #23 : Radius And Diameter

Determine the radius of the circle with a diameter of 6x+3 .

Possible Answers:

12x+3

3x+3

3x+1

12x+6

$3x+\frac{3}{2}$

Correct answer:

$3x+\frac{3}{2}$

Explanation:

The radius is half the diameter. Multiply the given diameter by half.

$\frac{1}{2}(6x+3) = 3x+\frac{3}{2}$

The answer is: $3x+\frac{3}{2}$

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Example Question #21 : Radius And Diameter

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

Possible Answers:

2.25m

0.75 m

3 m

4.5m

Correct answer:

0.75 m

Explanation:

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

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

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Example Question #992 : Ged Math

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 radius of the circles?

Possible Answers:

1.75cm

5cm

1.25cm

3.5cm

Correct answer:

1.25cm

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 radius of the circles?

Recall that your radius is always exactly half of the diameter. A diameter spans the entire width of a circle, while a radius goes from the center to the edge.

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

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

So, our answer is 1.25cm

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Example Question #21 : Geometry And Graphs

What is the radius of a circle if it has a circumference of 19.2 ?

Possible Answers:

3.14

4.3

3.6

3.1

2.2

Correct answer:

3.1

Explanation:

In order to solve this problem, it's important to understand the relationship between the two terms mentioned: radius and circumference.

The circumference of a circle can be solved for with the formula: $C= 2 \pi r$ , where r is radius. By substituting the circumference value into the equation, we should be able to solve for the radius fairly quickly.

$19.2=2 \pi r$

$\frac{19.2}{2 \pi}=r$

r = 3.1

Therefore, the radius of the circle is 3.1

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Example Question #30 : Geometry And Graphs

If a circle has a circumference of 37.4 , what is its radius?

Possible Answers:

5.8

4.7

6.0

6.1

7.0

Correct answer:

6.0

Explanation:

In order to solve this problem, it's important to understand the relationship between the two terms mentioned: radius and circumference.

$37.4=2 \pi r$

$\frac{37.4}{2 \pi}=r$

r = 6.0

Therefore, the radius of the circle is 6.0

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GED Math : Circles

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #21 : Circles

Example Question #21 : Circles

Example Question #23 : Geometry And Graphs

Example Question #22 : Circles

Example Question #21 : Geometry And Graphs

Example Question #23 : Radius And Diameter

Example Question #21 : Radius And Diameter

Example Question #992 : Ged Math

Example Question #21 : Geometry And Graphs

Example Question #30 : Geometry And Graphs

All GED Math Resources

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