### All ACT Math Resources

## Example Questions

### Example Question #161 : Plane Geometry

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

**Possible Answers:**

18

36

6

9

**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 #162 : Plane Geometry

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:**

7

√12

6

4

**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 #41 : Plane Geometry

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:**

4.70 inches

5.43 inches

3.06 inches

9.39 inches

14.75 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 #1 : 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:**

8

5

4

16

**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 #3 : Radius

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

**Possible Answers:**

14 inches

7 inches

16 inches

24.5 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 .

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