### All High School Math Resources

## Example Questions

### Example Question #1 : 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 #6 : 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:**

4.70 inches

5.43 inches

14.75 inches

3.06 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 #111 : Geometry

If the circumference of a circle is , what is the radius?

**Possible Answers:**

**Correct answer:**

The formula for circumference is .

Plug in our given information.

Divide both sides by .

### Example Question #62 : Radius

Find the radius of a circle with area .

**Possible Answers:**

**Correct answer:**

Since the formula for the area of a triangle is

plug in the given area and isolate for . This yields 13.

### Example Question #63 : Radius

The circumference of a circle is 45 inches. The circle's radius is ____ inches.

**Possible Answers:**

**Correct answer:**

When you know the circumference of a circle, you can determine its diameter by dividing the circumference by . Then, when you have the diameter, you can determine the radius by dividing the diameter by 2.

### 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

16

4

**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 Circumference

A circle has radius . What is the circumference, rounded to the nearest tenth?

**Possible Answers:**

**Correct answer:**

Circumference is given by the equation . We can use this equation with the given radius, 4.2, to solve for the circumference.

### Example Question #121 : Plane Geometry

What is the circumference of a circle with a radius of 12?

What is the circumference of a circle with a radius of 12?

**Possible Answers:**

**Correct answer:**

To find the circumference of a circle given the radius we must first know the equation for the circumference of a circle which is

We then plug in the number for the radius into the equation yielding

We multiply to find the value for the circumference is .

The answer is .

### 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:**

26*π*

2√13*π*

13*π*

√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*.