### All PSAT Math Resources

## Example Questions

### Example Question #1 : How To Find Circumference

Find the circumference of a circle with a radius of 9 feet.

**Possible Answers:**

8 π

18 π

9 π

81π

**Correct answer:**

18 π

To solve this question, use the equation for circumference, C=2πr. If you square 9, you will get 81π. If you forget to multiply 9 by 2, you will get option 9π.

### Example Question #2 : How To Find Circumference

If a circle has an area of , what is the circumference of the circle?

**Possible Answers:**

**Correct answer:**

The formula for the area of a circle is πr^{2}. For this particular circle, the area is 81π, so 81π = πr^{2}. Divide both sides by π and we are left with r^{2}=81. Take the square root of both sides to find r=9. The formula for the circumference of the circle is 2πr = 2π(9) = 18π. The correct answer is 18π.

### Example Question #1 : How To Find Circumference

A circle with an area of 13*π* in^{2} is centered at point *C*. What is the circumference of this circle?

**Possible Answers:**

13*π*

√26*π*

√13*π*

2√13*π*

26*π*

**Correct answer:**

2√13*π*

The formula for the area of a circle is *A *= *πr*^{2}.

We are given the area, and by substitution we know that 13*π *= *πr*^{2}.

We divide out the *π* and are left with 13 = *r*^{2}.

We take the square root of *r* to find that *r* = √13.

We find the circumference of the circle with the formula *C *= 2*πr*.

We then plug in our values to find *C *= 2√13*π*.

### Example Question #3 : How To Find Circumference

A 6 by 8 rectangle is inscribed in a circle. What is the circumference of the circle?

**Possible Answers:**

12*π*

6*π*

25*π*

8*π*

10*π*

**Correct answer:**

10*π*

First you must draw the diagram. The diagonal of the rectangle is also the diameter of the circle. The diagonal is the hypotenuse of a multiple of 2 of a 3,4,5 triangle, and therefore is 10.

Circumference = *π * *diameter = 10*π*.

### Example Question #1 : How To Find Circumference

A gardener wants to build a fence around their garden shown below. How many feet of fencing will they need, if the length of the rectangular side is 12 and the width is 8?

**Possible Answers:**

4π + 24

96 ft

40 ft.

8π + 24

**Correct answer:**

8π + 24

The shape of the garden consists of a rectangle and two semi-circles. Since they are building a fence we need to find the perimeter. The perimeter of the length of the rectangle is 24. The perimeter or circumference of the circle can be found using the equation C=2π(r), where r= the radius of the circle. Since we have two semi-circles we can find the circumference of one whole circle with a radius of 4, which would be 8π.

### Example Question #2 : How To Find Circumference

The diameter of a circle is defined by the two points (2,5) and (4,6). What is the circumference of this circle?

**Possible Answers:**

None of the other answers

π√5

2.5π

π√2.5

5π

**Correct answer:**

π√5

We first must calculate the distance between these two points. Recall that the distance formula is:√((x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2})

For us, it is therefore: √((4 - 2)^{2} + (6 - 5)^{2}) = √((2)^{2} + (1)^{2}) = √(4 + 1) = √5

If d = √5, the circumference of our circle is πd, or π√5.

### Example Question #4 : How To Find Circumference

A car tire has a radius of 18 inches. When the tire has made 200 revolutions, how far has the car gone in feet?

**Possible Answers:**

3600π

300π

600π

500π

**Correct answer:**

600π

If the radius is 18 inches, the diameter is 3 feet. The circumference of the tire is therefore 3π by C=d(π). After 200 revolutions, the tire and car have gone 3π x 200 = 600π feet.

### Example Question #3 : How To Find Circumference

A circle has the equation below. What is the circumference of the circle?

(*x* – 2)^{2} + (*y* + 3)^{2} = 9

**Possible Answers:**

**Correct answer:**

The radius is 3. Yielding a circumference of .

### Example Question #4 : How To Find Circumference

If a circle (shown above) with area is divided into 6 equal slices, what is the arc length of one of the slices?

Note: The above figure is not necessarily drawn to scale.

**Possible Answers:**

**Correct answer:**

Begin by solving for the circumference of the circle. Use the area of the circle, which is given, and the equation for the area of a circle to determine the radius of the circle:

=

Divide both sides by .

=

Solve for :

The radius of the circle is 6. Now find the circumference.

Circumference is equal to 2 times the radius multiplied by .

Now that we have the circumference, divide by 6 to find the length of one of the slices of the circle:

The arc length of one of the slices of the circle is .

### All PSAT Math Resources

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