GED Math : GED Math

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #2 : Circumference

What is the circumference of a circle with a diameter of 40?

Possible Answers:

\(\displaystyle 30\pi\)

\(\displaystyle 10\pi\)

\(\displaystyle 40\pi\)

\(\displaystyle 20\pi\)

Correct answer:

\(\displaystyle 40\pi\)

Explanation:

To find the circumference given the diameter we use the equation: 

\(\displaystyle C=D\pi\)

Then we substitute 40 in for our diameter:

\(\displaystyle C=40\pi\)

Example Question #7 : Circumference

Find the radius of a circle given that the circumference is \(\displaystyle 24\pi\).

Possible Answers:

16

5

12

24

Correct answer:

12

Explanation:

The equation of the circumference of a circle is as follows:

\(\displaystyle C=2\pi r\)

Now we substitute in our circumference and solve for radius:

\(\displaystyle 24\pi=2\pi r\)

\(\displaystyle 12=r\)

Example Question #5 : Circumference

What is the circumference of a circle with a radius of 4?

Possible Answers:

\(\displaystyle 4\pi\)

\(\displaystyle 8\pi\)

\(\displaystyle 12\pi\)

\(\displaystyle 16\pi\)

Correct answer:

\(\displaystyle 8\pi\)

Explanation:

We use the equation for the circumference of a circle: \(\displaystyle C=2\pi r\)

Now we substitute in our radius of 4:

\(\displaystyle C=2(4)\pi\)

\(\displaystyle C=8\pi\)

Example Question #6 : Circumference

If the area of a circle is \(\displaystyle 81\pi\), what is its circumference?

Possible Answers:

Cannot be computed from the information provided

\(\displaystyle 324\pi\)

\(\displaystyle 9\pi\)

\(\displaystyle 18\pi\)

\(\displaystyle 27\pi\)

Correct answer:

\(\displaystyle 18\pi\)

Explanation:

To solve this, you should first figure out your radius.  Remember that the area of a circle is defined as:

\(\displaystyle A=\pi r^2\)

For your data, you know that this is:

\(\displaystyle 81\pi=\pi r^2\)

Solving for \(\displaystyle r\), you get:

\(\displaystyle 81=r^2\), or

\(\displaystyle r=9\)

Now, recall that the circumference of a circle is defined as:

\(\displaystyle C=2\pi r\)

For your data, this is:

\(\displaystyle C=2\pi * 9 = 18\pi\)

Example Question #7 : Circumference

The area of a sector of a circle with a \(\displaystyle 90\) degree angle is \(\displaystyle 4\pi\).  What is the circumference of this circle?

Possible Answers:

Cannot be computed from the information provided

\(\displaystyle 8\pi\)

\(\displaystyle 16\pi\)

\(\displaystyle 12\pi\)

\(\displaystyle 4\pi\)

Correct answer:

\(\displaystyle 8\pi\)

Explanation:

\(\displaystyle 90\) degree angle represents one fourth of a full circle.  Therefore, the total area of this circle is \(\displaystyle 4 * 4\pi\) or \(\displaystyle 16\pi\).  Now, recall your area formula:

\(\displaystyle A=\pi r^2\)

For your data, this means:

\(\displaystyle 16\pi = \pi r^2\)

Solving for \(\displaystyle r\), you get:

\(\displaystyle 16=r^2\) or \(\displaystyle r=4\)

Now, the circumference of a circle is defined as:

\(\displaystyle C=2\pi r\)

For your data, this is:

\(\displaystyle C=2*4*\pi=8\pi\)

Example Question #11 : Circumference

What is the circumference of the circle with an area of 5?

Possible Answers:

\(\displaystyle 10\sqrt{\pi}\)

\(\displaystyle 2\pi \sqrt{5\pi}\)

\(\displaystyle 2\sqrt{5\pi}\)

\(\displaystyle \textup{The answer is not given.}\)

\(\displaystyle \sqrt{10\pi}\)

Correct answer:

\(\displaystyle 2\sqrt{5\pi}\)

Explanation:

Write the formula for the area of a circle.

\(\displaystyle A =\pi r^2\)

Substitute the area.

\(\displaystyle 5 =\pi r^2\)

Divide by pi on both sides.

\(\displaystyle \frac{5}{\pi } =\frac{\pi r^2}{\pi }\)

\(\displaystyle r^2 = \frac{5}{\pi}\)

Square root both sides.

\(\displaystyle \sqrt{r^2} = \sqrt{\frac{5}{\pi}}\)

\(\displaystyle r = \sqrt{\frac{5}{\pi}}\)

Write the circumference formula for the circle, and substitute the radius.

\(\displaystyle C=2\pi r =2\pi \sqrt{\frac{5}{\pi}} = 2\pi \frac{\sqrt{5}}{\sqrt{\pi}}\)

Since \(\displaystyle \pi = (\sqrt{\pi} \cdot \sqrt{\pi})\), we can eliminate the denominator by rewriting \(\displaystyle \pi\).

\(\displaystyle 2\pi \frac{\sqrt{5}}{\sqrt{\pi}} = 2(\sqrt{\pi}\cdot \sqrt{\pi}) \frac{\sqrt{5}}{\sqrt{\pi}} = 2\sqrt{\pi}\cdot \sqrt{5}\)

 

The answer is:  \(\displaystyle 2\sqrt{5\pi}\)

Example Question #11 : Circumference

Find the circumference of a circle with an area of \(\displaystyle 12\pi\).

Possible Answers:

\(\displaystyle 2\pi \sqrt6\)

\(\displaystyle 4\pi\)

\(\displaystyle 4\pi \sqrt3\)

\(\displaystyle 2\pi \sqrt3\)

\(\displaystyle 3\pi \sqrt{2}\)

Correct answer:

\(\displaystyle 4\pi \sqrt3\)

Explanation:

Write the formula for the area of a circle, and substitute the area into the formula.

\(\displaystyle A=\pi r^2\)

\(\displaystyle 12\pi =\pi r^2\)

Divide by pi on both sides.

\(\displaystyle \frac{12\pi }{\pi}=\frac{\pi r^2}{\pi}\)

\(\displaystyle r^2 = 12\)

Square root both sides.

\(\displaystyle \sqrt{r^2 }= \sqrt{12}\)

\(\displaystyle r=2\sqrt{3}\)

Write the formula for the circumference of the circle.

\(\displaystyle C=2\pi r\)

Substitute the radius into the equation.

\(\displaystyle C=2\pi (2\sqrt3) = 4\pi \sqrt3\)

The answer is:  \(\displaystyle 4\pi \sqrt3\)

Example Question #12 : Circumference

Find the circumference of a circle with a diameter of \(\displaystyle 5\pi^2\).

Possible Answers:

\(\displaystyle 5\pi ^3\)

\(\displaystyle \frac{25}{4}\pi ^4\)

\(\displaystyle 10\pi ^3\)

\(\displaystyle 10\pi ^2\)

\(\displaystyle \frac{25}{4}\pi ^3\)

Correct answer:

\(\displaystyle 5\pi ^3\)

Explanation:

Write the formula for the circumference.

\(\displaystyle C=\pi D\)

Substitute the diameter into the equation.

\(\displaystyle C=\pi (5\pi^2) = 5\pi ^3\)

The answer is:  \(\displaystyle 5\pi ^3\)

Example Question #51 : 2 Dimensional Geometry

Find the circumference of a circle with a diameter of 14cm.

Possible Answers:

\(\displaystyle 7\pi \text{ cm}\)

\(\displaystyle 196\pi \text{ cm}\)

\(\displaystyle 49\pi \text{ cm}\)

\(\displaystyle 14\pi \text{ cm}\)

\(\displaystyle 28\pi \text{ cm}\)

Correct answer:

\(\displaystyle 14\pi \text{ cm}\)

Explanation:

To find the circumference of a circle, we will use the following formula:

\(\displaystyle C = \pi d\)

where d is the diameter of the circle.

Now, we know the diameter of the circle is 14cm. So, we will substitute. We get

\(\displaystyle C = \pi \cdot 14\text{cm}\)

\(\displaystyle C = 14\pi \text{ cm}\)

Example Question #51 : Circles

Identify the circumference of the circle with an area of \(\displaystyle 12 \pi\).

Possible Answers:

\(\displaystyle 2\pi \sqrt{3}\)

\(\displaystyle \frac{4\pi \sqrt{3}}{3}\)

\(\displaystyle \frac{3\pi \sqrt{3}}{2}\)

\(\displaystyle 4\pi \sqrt{3}\)

\(\displaystyle \frac{2\pi \sqrt{3}}{3}\)

Correct answer:

\(\displaystyle 4\pi \sqrt{3}\)

Explanation:

Write the formula for the area of a circle.

\(\displaystyle A=\pi r^2\)

Substitute the area.

\(\displaystyle 12\pi=\pi r^2\)

\(\displaystyle r^2=12\)

Square root both sides to find the radius.

\(\displaystyle \sqrt{r^2}=\sqrt{12}\)

\(\displaystyle r=\sqrt{12} = \sqrt{4}\times \sqrt{3} = 2\sqrt{3}\)

Write the formula for the circumference of the circle.

\(\displaystyle C=2\pi r = 2\pi(2\sqrt{3}) = 4\pi \sqrt{3}\)

The answer is:  \(\displaystyle 4\pi \sqrt{3}\)

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