### All SAT II Math II Resources

## Example Questions

### Example Question #31 : 2 Dimensional Geometry

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

**Possible Answers:**

**Correct answer:**

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 #2 : Diameter, Radius, And Circumference

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

**Possible Answers:**

**Correct answer:**

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 #31 : 2 Dimensional Geometry

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

**Possible Answers:**

**Correct answer:**

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:**

Write the formula for the circumference of a circle.

Substitute the diameter into the equation.

The answer is:

### Example Question #1 : Diameter, Radius, And Circumference

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

**Possible Answers:**

**Correct answer:**

The diameter of a circle is twice the radius.

Substitute the radius.

The answer is:

### Example Question #31 : 2 Dimensional Geometry

Determine the radius if the circumference of a circle is .

**Possible Answers:**

**Correct answer:**

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:**

Write the formula for the circumference of a circle.

Substitute the circumference.

Multiply by on both sides to isolate .

The radius is:

### Example Question #1 : Diameter, Radius, And Circumference

Determine the diameter if the radius of a circle is .

**Possible Answers:**

**Correct answer:**

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

The answer is:

### Example Question #1 : Diameter, Radius, And Circumference

Determine the circumference of a circle with a radius of .

**Possible Answers:**

**Correct answer:**

The circumference of a circle is:

Substitute the radius.

The answer is: