### All SAT Math Resources

## Example Questions

### Example Question #42 : Plane Geometry

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 #2 : 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*

2√13*π*

26*π*

13*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 #1 : 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*

10*π*

8*π*

25*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:**

40 ft.

96 ft

8π + 24

4π + 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 #1 : 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:**

2.5π

None of the other answers

π√5

5π

π√2.5

**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 #1 : 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:**

500π

3600π

600π

300π

**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 #2 : 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 #1 : How To Find Circumference

Find the circumferencce fo a circle given radius of 7.

**Possible Answers:**

**Correct answer:**

To solve, simply use the formula for the circumference of a circle. Thus,

Like the prior question, it is important to think about dimensions if you don't remember the exact formula. Circumference is 1 dimensional, so it makes sense that the variable is not squared as cubed. If you rather, you can use the following formula, but realize by defining diameter, it equals the prior one.

Thus,

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

The area of a circle is . What is its circumference?

**Possible Answers:**

None of the given answers.

**Correct answer:**

First, let's find the radius r of the circle by using the given area.

Now, plug this radius into the formula for a circle's circumference.

.

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

The surface area of a sphere is .

is a point on the surface of the sphere; is the point on the sphere farthest from . A curve is drawn from to entirely on the surface of the sphere. Give the length of the shortest possible curve fitting this description.

**Possible Answers:**

**Correct answer:**

Below is a sphere with its center and with points and as described.

For and to be on the surface of the sphere and to be a maximum distance apart, they must be endpoints of a diameter of the sphere. The shortest curve connecting them that is entirely on the surface is a semicircle whose radius coincides with that of the sphere. Therefore, first find the radius of the sphere using the surface area formula

Setting and solving for :

The length of the curve is half the circumference of a circle with radius 10, or

Substituting 10 for , this is

.

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