SAT II Math II : Diameter, Radius, and Circumference

Study concepts, example questions & explanations for SAT II Math II

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Example Questions

Example Question #1 : Diameter, Radius, And Circumference

If a particle accelerator has a circumference of , what is its radius?

Possible Answers:

Correct answer:

Explanation:

If a particle accelerator has a circumference of , what is its radius?

Begin with the formula for the circumference of a circle:

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

Divide both sides by 2 pi to get out answer:

Example Question #1 : Diameter, Radius, And Circumference

If a particle accelerator has a circumference of , what is its diameter?

Possible Answers:

Correct answer:

Explanation:

If a particle accelerator has a circumference of , what is its radius?

Begin with the formula for circumference of a circle:

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:

Now, plug in our circumference and solve for d:

Divide both sides by pi to get:

So our answer is 18.5 miles

Example Question #2 : Diameter, Radius, And Circumference

If the circumference of a circle is , what must be the diameter?

Possible Answers:

Correct answer:

Explanation:

Write the circumference formula for the circle.

Substitute the circumference into the equation.

Divide by  on both sides.

The diameter is twice the radius.

The answer is:  

Example Question #4 : Diameter, Radius, And Circumference

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

Possible Answers:

Correct answer:

Explanation:

Write the formula for the circumference of a circle.

Substitute the diameter into the equation.

The answer is:  

Example Question #3 : Diameter, Radius, And Circumference

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

Possible Answers:

Correct answer:

Explanation:

The diameter of a circle is twice the radius.

Substitute the radius.

The answer is:  

Example Question #6 : Diameter, Radius, And Circumference

Determine the radius if the circumference of a circle is .

Possible Answers:

Correct answer:

Explanation:

Write the formula for the circumference of a circle.

Substitute the circumference.

Divide by  on both sides.

Reduce both sides.

The answer is:  

Example Question #7 : Diameter, Radius, And Circumference

Determine the radius of a circle if the circumference is .

Possible Answers:

Correct answer:

Explanation:

Write the formula for the circumference of a circle.

Substitute the circumference.

Multiply by  on both sides to isolate .

The radius is:  

Example Question #4 : Diameter, Radius, And Circumference

Determine the diameter if the radius of a circle is .

Possible Answers:

Correct answer:

Explanation:

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

The answer is:  

Example Question #9 : Diameter, Radius, And Circumference

Determine the circumference of a circle with a radius of .

Possible Answers:

Correct answer:

Explanation:

The circumference of a circle is:  

Substitute the radius.

The answer is:  

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