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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #2 : 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:

Correct answer:

Explanation:

We know that the formula for the area of a circle is πr². Therefore, we must set 36π equal to this formula to solve for the radius of the circle.

36π = πr²

36 = r²

6 = r

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Example Question #3 : 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?

Act_math_170_02

Circle X

Possible Answers:

√12

Correct answer:

Explanation:

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 = πr²

36 = r²

√36 = r

6 = r

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Example Question #4 : 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:

5.43 inches

9.39 inches

14.75 inches

4.70 inches

3.06 inches

Correct answer:

4.70 inches

Explanation:

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)

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

What is the name of the segment in red?

Possible Answers:

Radius

Diameter

Chord

Diagonal

Ray

Correct answer:

Radius

Explanation:

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

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

What is the name of the segment in brown?

Possible Answers:

Ray

Diagonal

Diameter

Chord

Radius

Correct answer:

Chord

Explanation:

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

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Example Question #3 : 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:

Explanation:

The radius is half of the diameter. To find the radius, simply divide the diameter by 2.

16/2=8

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Example Question #111 : Circles

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:

Correct answer:

Explanation:

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.

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Example Question #4 : How To Find The Length Of A Radius

The circle shown below has an area equal to $49\pi$ . What is the length of the radius, , of this circle?

Circle

Possible Answers:

Cannot be determined.

$7\pi$

Correct answer:

Explanation:

The formula for the area of a circle is $A=\pi R^{2}$ . We can fill in what we know, the area, and then solve for the radius, .

$49\pi =\pi R^{2}$

Divide each side of the equation by $\pi$ :

$49=R^{2}$

Take the square root of each side:

$\sqrt{49}=\sqrt{R^{2}}$

R=7

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Example Question #1 : Radius

A circle has an area of $49\pi \ in^{2}$ . What is the radius of the circle, in inches?

Possible Answers:

49 inches

7 inches

16 inches

24.5 inches

14 inches

Correct answer:

7 inches

Explanation:

We know that the formula for the area of a circle is πr². Therefore, we must set 49π equal to this formula to solve for the radius of the circle.

49π = πr²

49 = r²

7 = r

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Example Question #161 : Plane Geometry

Find the length of the radius given the circumference is 16

Possible Answers:

$8\pi$

$4\pi$

$\frac{8}{\pi}$

Correct answer:

$\frac{8}{\pi}$

Explanation:

To solve, simply use the formula of the circumference and solve for r. Thus,

$C=2\pi{r}\Rightarrow r=\frac{C}{2\pi}$

$r=\frac{16}{2\pi}=\frac{8}{\pi}$

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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

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

Example Question #3 : How To Find The Length Of A Radius

Example Question #4 : How To Find The Length Of A Radius

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

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

Example Question #3 : How To Find The Length Of A Radius

Example Question #111 : Circles

Example Question #4 : How To Find The Length Of A Radius

Example Question #1 : Radius

Example Question #161 : Plane Geometry

All Basic Geometry Resources

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