Radius and Diameter - GED Math

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Question

What is the radius, in inches, of a circle with a diameter of 12 inches?

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Answer

The radius is half of the diameter:

From here we plug in our diameter measure of 12 and solve for the radius:

$\frac{12}{2}=r$

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Question

What is the diameter of a circle with radius of 10 inches?

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Answer

The diameter is twice the radius:

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Question

What is the radius of a circle that has a circumference of $36\pi$ ?

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Answer

The equation for circumference of a circle is as follows:

$C=2 \pi r$

Plug in the given values and solve for the radius:

$36\pi=2\pi r$

Now we divide each side by $2\pi$ :

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Question

Find the diameter of a circle that has a circumference of $25\pi$ ?

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Answer

We know the equation for the circumference of a circle is $C=2\pi r$ . We also know that the the diameter is the twice the radius, so we can write $C=D\pi$ .

Plug in the given values and solve:

$25\pi=D\pi$

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Question

What is the diameter of a circle with an area of $144\pi$ ?

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Answer

In order to solve this question, start by finding the radius. Recall that the area of a circle is computed as:

$A=\pi r^2$

For our data, this is:

$144\pi = \pi r^2$

Solving for , we get:

or

Now, recall that the diameter is double the radius. Thus, it is .

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Question

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

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Answer

Recall that the circumference formula is:

$C=2\pi r$

Now, for your data, this gives you:

$17=\pi r$

You need to be careful, for some students get confused when they have to divide by $\pi$ . However, just treat it like any other number or variable. This means that you can solve for and get:

$r=\frac{17}{\pi}$

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Question

What is the diameter of a circle given the area of 30?

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Answer

Write the area formula of a circle.

$A=\pi r^2$

Substitute the area.

$30=\pi r^2$

Divide by pi on both sides.

$\frac{30}{\pi}=\frac{\pi r^2}{\pi}$

$r^2 = \frac{30}{\pi}$

Square root both sides.

$\sqrt{r^2} =\sqrt{ \frac{30}{\pi}}$

$r=\sqrt{ \frac{30}{\pi}}$

The radius is: $\sqrt{\frac{30}{\pi}}$

The diameter is double the radius.

The answer is: $2\sqrt{\frac{30}{\pi}}$

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Question

What is the diameter of a circle if the area is $14\pi$ ?

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Answer

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the area into the equation.

$14\pi=\pi r^2$

Divide by pi on both sides.

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

$r=\sqrt{14}$

The diameter is twice the radius.

The answer is: $2\sqrt{14}$

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Question

If the diameter of a circle is 12 feet, what is the radius in yards?

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Answer

There are three feet in one yard.

Using dimensional analysis, we can determine the given diameter in yards first.

$12 \textup{ ft}(\frac{1 \textup{ yd}}{3 \textup{ ft}}) = 4 \textup{ yds}$

The radius is half the diameter.

The answer is: $2 \textup{ yds}$

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Question

Determine the diameter if the radius is $\frac{2}{3}x-4$ .

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Answer

The diameter is double the radius.

$2(\frac{2}{3}x-4) = \frac{4}{3}x-8$

The answer is: $\frac{4}{3}x-8$

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Question

Determine the diameter of a circle if the radius is $2\frac{1}{3}$ .

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Answer

The diameter is twice the radius.

Convert the mixed fraction to an improper fraction.

$D= 2(\frac{7}{3}) = \frac{14}{3}$

The answer is: $\frac{14}{3}$

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Question

Determine the diameter if the radius is $\frac{1}{8}$ .

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Answer

The diameter is twice the radius.

Multiply the radius by two.

$\frac{1}{8} (2) = \frac{2}{8} = \frac{1}{4}$

The answer is: $\frac{1}{4}$

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Question

What is the radius if the diameter of a circle is $\frac{\sqrt3}{3}$ ?

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Answer

The radius is half the diameter of a circle.

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

This is also similar to multiply diameter by one-half.

$\frac{\sqrt3}{3} \times \frac{1}{2} = \frac{\sqrt{3}}{6}$

The answer is: $\frac{\sqrt{3}}{6}$

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Question

What is the radius with a diameter of $\frac{\sqrt3}{2}$ ?

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Answer

The radius is half the diameter.

Multiply the diameter by one-half.

$\frac{\sqrt3}{2} \cdot \frac{1}{2} = \frac{\sqrt3}{4}$

The answer is: $\frac{\sqrt3}{4}$

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Question

Find the radius of a circle with an area of $8\pi$ .

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Answer

Write the formula for the area of a circle.

$A = \pi r^2$

Substitute the area.

$8\pi = \pi r^2$

Divide by pi on both sides.

$\frac{8\pi }{\pi}=\frac{ \pi r^2}{\pi}$

Square root both sides.

$\sqrt{r^2 }= \sqrt{8}$

$r= \sqrt8 = 2\sqrt2$

The answer is: $2\sqrt2$

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Question

Find the value of the diameter if the radius is $5\pi-2$ .

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Answer

The diameter is double the radius.

Multiply the quantity by two.

$2(5\pi-2) = 10\pi -4$

The answer is: $10\pi -4$

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Question

Determine the radius if the diameter is $\frac{\sqrt{2}}{3}$ .

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Answer

The radius is half the diameter.

Multiply the diameter by half.

$\frac{\sqrt{2}}{3} \cdot\frac{1}{2}$

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

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Question

Determine the radius of the circle if the diameter is $\frac{3\sqrt5}{7}$ .

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Answer

The radius is half the diameter. To find the radius, multiply the diameter by half.

$\frac{3\sqrt5}{7} \cdot \frac{1}{2} = \frac{3\sqrt5}{14}$

The answer is: $\frac{3\sqrt5}{14}$

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Question

Determine the radius of the circle if the diameter of a circle is $\frac{3}{50}$ .

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Answer

The radius is half the diameter.

Multiply the diameter by one-half.

$\frac{3}{50} \cdot \frac{1}{2} = \frac{3}{100}$

The answer is: $\frac{3}{100}$

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Question

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

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Answer

The diameter is double the radius.

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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