### All Basic Geometry Resources

## Example Questions

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

The area of a circle is one square yard. Give its radius in *inches,* to the nearest tenth of an inch.

**Possible Answers:**

**Correct answer:**

The area of a circle is

Substitute 1 for :

This is the radius in yards. The radius in inches is 36 times this.

20.3 inches is the radius.

### 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:**

36

6

9

18

**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 #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:**

√12

4

7

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 #2 : 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:**

9.39 inches

14.75 inches

3.06 inches

4.70 inches

5.43 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

What is the name of the segment in red?

**Possible Answers:**

Radius

Ray

Diagonal

Chord

Diameter

**Correct answer:**

Radius

The radius is the distance from the center of a circle to any point on it's perimeter.

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

What is the name of the segment in brown?

**Possible Answers:**

Diagonal

Radius

Diameter

Chord

Ray

**Correct answer:**

Chord

A chord is a line segment which joins two points on a curve. A chord does not go through the center of a circle.

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

The diameter of a circle is 16 centimeters. What is the circle's radius in centimeters?

**Possible Answers:**

**Correct answer:**

The radius is half of the diameter. To find the radius, simply divide 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:**

5

8

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 #3 : How To Find The Length Of A Radius

The circle shown below has an area equal to . What is the length of the radius, , of this circle?

**Possible Answers:**

Cannot be determined.

**Correct answer:**

The formula for the area of a circle is . We can fill in what we know, the area, and then solve for the radius, .

Divide each side of the equation by :

Take the square root of each side:

### 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:**

14 inches

49 inches

7 inches

16 inches

24.5 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*

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