### All ACT Math Resources

## Example Questions

### Example Question #13 : How To Find Circumference

Find the circumference of a circle with radius 6.

**Possible Answers:**

**Correct answer:**

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

In this particular case the radius of 6 should be substituted into the following equation to solve for the circumference.

Thus,

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

Ashley has a square room in her apartment that measures 81 square feet. What is the circumference of the largest circular area rug that she can fit in the space?

**Possible Answers:**

**Correct answer:**

In order to solve this question, first calculate the length of each side of the room.

The length of each side of the room is also equal to the length of the diameter of the largest circular rug that can fit in the room. Since , the circumference is simply

### Example Question #1 : How To Find The Length Of A Radius

A circle has an area of 36π inches. What is the radius of the circle, in inches?

**Possible Answers:**

18

9

6

36

**Correct answer:**

6

We know that the formula for the area of a circle is π*r*^{2}. Therefore, we must set 36π equal to this formula to solve for the radius of the circle.

36π = π*r*^{2}

36 = *r*^{2}

6 = r

### Example Question #2 : How To Find The Length Of A Radius

Circle X is divided into 3 sections: A, B, and C. The 3 sections are equal in area. If the area of section C is 12π, what is the radius of the circle?

Circle X

**Possible Answers:**

4

7

√12

6

**Correct answer:**

6

Find the total area of the circle, then use the area formula to find the radius.

Area of section A = section B = section C

Area of circle X = A + B + C = 12π+ 12π + 12π = 36π

Area of circle = where r is the radius of the circle

36π = πr^{2}

36 = r^{2}

√36 = r

6 = r

### Example Question #1 : How To Find The Length Of A Radius

The specifications of an official NBA basketball are that it must be 29.5 inches in circumference and weigh 22 ounces. What is the approximate radius of the basketball?

**Possible Answers:**

3.06 inches

5.43 inches

14.75 inches

4.70 inches

9.39 inches

**Correct answer:**

4.70 inches

To Find your answer, we would use the formula: C=2πr. We are given that C = 29.5. Thus we can plug in to get [29.5]=2πr and then multiply 2π to get 29.5=(6.28)r. Lastly, we divide both sides by 6.28 to get 4.70=r. (The information given of 22 ounces is useless)

### Example Question #2 : How To Find The Length Of A Radius

A circle with center (8, **–**5) is tangent to the y-axis in the standard (x,y) coordinate plane. What is the radius of this circle?

**Possible Answers:**

4

5

16

8

**Correct answer:**

8

For the circle to be tangent to the y-axis, it must have its outer edge on the axis. The center is 8 units from the edge.

### Example Question #1 : How To Find The Length Of A Radius

A circle has an area of . What is the radius of the circle, in inches?

**Possible Answers:**

24.5 inches

7 inches

14 inches

16 inches

49 inches

**Correct answer:**

7 inches

We know that the formula for the area of a circle is *πr*^{2}. Therefore, we must set 49*π* equal to this formula to solve for the radius of the circle.

49*π* = *πr*^{2}

49 = *r*^{2}

7 = *r*

### Example Question #1 : How To Find The Length Of A Radius

A circle has a circumference of . What is the radius of the circle, in feet?

**Possible Answers:**

**Correct answer:**

To answer this question we need to find the radius of the circle given the circumference of .

The equation for a circle's circumference is:

We can plug our circumference into this equation to find the diameter.

We can now divide both sides by

So our diameter is . To find the radius from the diameter, we use the following equation:

So, for this data:

Therefore, the radius of our circle is .