High School Math : Geometry

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #101 : Circles

A circle has a diameter of 13 cm.  What is the circle's circumference?

Possible Answers:

\displaystyle 134.45

\displaystyle 53.5

\displaystyle 40.84

\displaystyle 20.41

\displaystyle 26.75

Correct answer:

\displaystyle 40.84

Explanation:

To find the circumference of a circle, multiply the circle's diameter by \displaystyle \pi.

Example Question #102 : Circles

Find the circumference of the following circle:

21

Possible Answers:

\displaystyle 14 \pi\ m

 

\displaystyle 12 \pi\ m

\displaystyle 10 \pi\ m

\displaystyle 16 \pi\ m

\displaystyle 8 \pi\ m

Correct answer:

\displaystyle 14 \pi\ m

 

Explanation:

The formula for the circumference of a circle is

\displaystyle C = 2 \pi (r),

where \displaystyle r is the radius of the circle.

Plugging in our values, we get:

\displaystyle C = 2\pi (7\ m)

\displaystyle C = 14 \pi\ m

Example Question #1 : How To Find Circumference

A car tire has a radius of 18 inches. When the tire has made 200 revolutions, how far has the car gone in feet?

Possible Answers:

500π

600π

300π

3600π

Correct answer:

600π

Explanation:

If the radius is 18 inches, the diameter is 3 feet. The circumference of the tire is therefore 3π by C=d(π). After 200 revolutions, the tire and car have gone 3π x 200 = 600π feet.

Example Question #14 : Radius

A circle has the equation below. What is the circumference of the circle?

(x – 2)2 + (y + 3)2 = 9

Possible Answers:

\displaystyle 6\pi

\displaystyle 16\pi

\displaystyle 9\pi

\displaystyle 3\pi

Correct answer:

\displaystyle 6\pi

Explanation:

The radius is 3. Yielding a circumference of \displaystyle 6\pi.

Example Question #351 : Sat Mathematics

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:

\displaystyle 8\pi

\displaystyle 18\pi

\displaystyle 81\pi

\displaystyle 10\pi

\displaystyle 9\pi

Correct answer:

\displaystyle 9\pi

Explanation:

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

\displaystyle A=s^2

\displaystyle 81=s^2

\displaystyle s=9

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 \displaystyle C=\pi d, the circumference is simply

\displaystyle C=9\pi

Example Question #1 : How To Find The Length Of The Diameter

What is the diameter of a circle with a circumference of \displaystyle 16\pi?

Possible Answers:

\displaystyle 4

\displaystyle 8

\displaystyle 16

\displaystyle 64

Correct answer:

\displaystyle 16

Explanation:

To find the diameter we must understand the diameter in terms of circumference. The equation for the circumference of a circle is \displaystyle C=D\pi, where \displaystyle C is the circumference and \displaystyle D is the diameter. The circumference is equal to the diameter multiplied by \displaystyle \pi.

We can rearrange \displaystyle C=D\pi to solve for \displaystyle D.

\displaystyle D=\frac{C}{\pi}

All we have to do is plug in the circumference and divide by \displaystyle \pi, and it will yield the diameter.

\displaystyle D=\frac{16\pi}{\pi}=16

The \displaystyle \pis cancel and the diameter is \displaystyle 16.

Example Question #131 : Plane Geometry

If the area of a circle is four times larger than the circumference of that same circle, what is the diameter of the circle?

Possible Answers:

4

16

8

2

32

Correct answer:

16

Explanation:

Set the area of the circle equal to four times the circumference πr2 = 4(2πr). 

Cross out both π symbols and one r on each side leaves you with r = 4(2) so r = 8 and therefore = 16.

Example Question #131 : Geometry

The perimeter of a circle is 36 π.  What is the diameter of the circle?

Possible Answers:

18

72

36

6

3

Correct answer:

36

Explanation:

The perimeter of a circle = 2 πr = πd

Therefore d = 36

Example Question #1 : Diameter And Chords

Sat_math_picture

If the area of the circle touching the square in the picture above is \displaystyle 81\pi, what is the closest value to the area of the square?

Possible Answers:

\displaystyle 162

\displaystyle 100

\displaystyle 81

\displaystyle 144

\displaystyle 211

Correct answer:

\displaystyle 162

Explanation:

Obtain the radius of the circle from the area.

\displaystyle A=\pi r^2=81\pi

\displaystyle r^2=81

\displaystyle r=9

Split the square up into 4 triangles by connecting opposite corners. These triangles will have a right angle at the center of the square, formed by two radii of the circle, and two 45-degree angles at the square's corners. Because you have a 45-45-90 triangle, you can calculate the sides of the triangles to be \displaystyle x, \displaystyle x, and \displaystyle x\sqrt{2}. The radii of the circle (from the center to the corners of the square) will be 9. The hypotenuse (side of the square) must be \displaystyle 9\sqrt{2}.

The area of the square is then \displaystyle (9\sqrt{2})^2=162.

Example Question #2 : Diameter

Two legs of a right triangle measure 3 and 4, respectively. What is the area of the circle that circumscribes the triangle? 

Possible Answers:

\displaystyle 6.25\pi

\displaystyle 6\pi

\displaystyle 25\pi

\displaystyle 5\pi

\displaystyle 12.5\pi

Correct answer:

\displaystyle 6.25\pi

Explanation:

For the circle to contain all 3 vertices, the hypotenuse must be the diameter of the circle. The hypotenuse, and therefore the diameter, is 5, since this must be a 3-4-5 right triangle.

The equation for the area of a circle is A = πr2.

\displaystyle A=\pi (5/2)^2=6.25\pi

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