Diameter, Radius, and Circumference - SAT Subject Test in Math II

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Question

If a particle accelerator has a circumference of $18.5 \pi mi$ , what is its radius?

Answer

If a particle accelerator has a circumference of $18.5 \pi mi$ , what is its radius?

Begin with the formula for the circumference of a circle:

$Circ=2 \pi r$

Now, we know the circumference, so just plug in and solve for r.

$18.5 \pi mi=2 \pi r$

Divide both sides by 2 pi to get out answer:

$18.5 \pi mi\div 2 \pi=2 \pi r\div 2\pi$

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Question

If a particle accelerator has a circumference of $18.5 \pi mi$ , what is its diameter?

Answer

If a particle accelerator has a circumference of $18.5 \pi mi$ , what is its radius?

Begin with the formula for circumference of a circle:

$C=2\pi r$

Now, we can see that 2r is really the same as d, right? Our radius will always be half the length of the diameter.

So, we can rewrite the above equation as:

$C=d \pi$

Now, plug in our circumference and solve for d:

$18.5 \pi mi=d \pi$

Divide both sides by pi to get:

So our answer is 18.5 miles

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Question

If the circumference of a circle is $2\pi +1$ , what must be the diameter?

Answer

Write the circumference formula for the circle.

$C=2\pi r$

Substitute the circumference into the equation.

$2\pi +1 = 2\pi r$

Divide by $2\pi$ on both sides.

$\frac{2\pi +1}{ 2\pi } =\frac{ 2\pi r}{ 2\pi }$

$r=\frac{2\pi +1}{ 2\pi }$

The diameter is twice the radius.

$d=2r=2\cdot \frac{2\pi +1}{ 2\pi } = \frac{2\pi+1}{\pi}$

The answer is: $\frac{2\pi+1}{\pi}$

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Question

What is the circumference of a circle with a diameter of $\frac{\pi }{4}$ ?

Answer

Write the formula for the circumference of a circle.

$C= \pi D$

Substitute the diameter into the equation.

$C= \pi (\frac{\pi}{4}) = \frac{\pi^2}{4}$

The answer is: $\frac{\pi^2}{4}$

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Question

What is the diameter of the circle with a radius of $2\sqrt{10}$ ?

Answer

The diameter of a circle is twice the radius.

Substitute the radius.

$D=2(2\sqrt{10}) = 4\sqrt{10}$

The answer is: $4\sqrt{10}$

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Question

Determine the radius if the circumference of a circle is $2\sqrt2$ .

Answer

Write the formula for the circumference of a circle.

$C=2\pi r$

Substitute the circumference.

$2\sqrt2=2\pi r$

Divide by $2\pi$ on both sides.

$\frac{2\sqrt2}{2\pi }=\frac{2\pi r}{2\pi }$

Reduce both sides.

The answer is: $r= \frac{\sqrt2}{\pi}$

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Question

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

Answer

Write the formula for the circumference of a circle.

$C=2\pi r$

Substitute the circumference.

$\frac{2}{3}\pi=2\pi r$

Multiply by $\frac{1}{2\pi}$ on both sides to isolate .

$\frac{2}{3}\pi\cdot \frac{1}{2\pi}=2\pi r \cdot \frac{1}{2\pi}$

$r= \frac{1}{3}$

The radius is: $\frac{1}{3}$

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Question

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

Answer

The diameter is double the radius. Multiply the radius by two.

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

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

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Question

Determine the circumference of a circle with a radius of $\frac{2}{\pi}$ .

Answer

The circumference of a circle is: $C=2\pi r$

Substitute the radius.

$C=2\pi (\frac{2}{\pi})$

The answer is:

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