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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #371 : Basic Geometry

Use 3.14 for Pi in the following question.

If the circumference of a circle is 25.12cm, what is the measure of its diameter?

Possible Answers:

$12.5\text{ cm}$

$11.3\text{ cm}$

$8\text{ cm}$

$6\text{ cm}$

$21.98\text{ cm}$

Correct answer:

$8\text{ cm}$

Explanation:

First we need to know that the formula for circumference of a circle is

$\text{Circumference}=\text{Diameter}\cdot \pi$ .

Since we know the circumference, we can plug it into our equation, along with pi, and solve for diameter.

$25.12cm=D\cdot3.14$

To solve for D (diameter) we must divide both sides by pi

$25.12cm\div3.14=D$

when we divide 25.12 by 3.14 we get 8, so our final answer is 8cm.

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Example Question #372 : Basic Geometry

A circular pizza has an area of $36\pi$ square inches. What is its diameter in inches?

Possible Answers:

Correct answer:

Explanation:

The area of a circle with a given radius is $A=\pi r^2$ . Since the area of the circular pizza is given as $36\pi$ square inches, we can solve for its radius as follows:

$36\pi=\pi r^2$

$\Rightarrow 36 = r^2$

$\Rightarrow r = \sqrt{36} = 6$

Now that we know that the radius of the pizza is inches, we can now deduce its diameter knowing that the diameter of a circle is equal to twice its radius. Hence, the diameter of this pizza is 2(6)=12 inches.

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Example Question #1 : Diameter And Chords

Let represent the area of a circle and represent its circumference. Which of the following equations expresses in terms of ?

Possible Answers:

C^2

Correct answer:

Explanation:

The formula for the area of a circle is $A=\pi r^2$ , and the formula for circumference is $C=2\pi r$ . If we solve for C in terms of r, we get
$r=C/2\pi$ .

We can then substitute this value of r into the formula for the area:

$A=\pi r^2$

$=\pi (C/2\pi )^2$

$=C^2\pi /4\pi ^2$

$=C^2/4\pi$

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Example Question #1 : How To Find The Ratio Of Diameter And Circumference

A can of soup has a base area of $16\pi$ . What is the ratio of the can's diameter to its circumference?

Possible Answers:

$\frac{1}{2\pi}$

$\frac{\pi}{8}$

$\frac{\pi}{1}$

$\frac{2\pi}{1}$

$\frac{1}{\pi}$

Correct answer:

$\frac{1}{\pi}$

Explanation:

If the cirlcle has an area of $16\pi$ then we need to find a way to determine the diameter of the circle. We must do 4 things:

1. Find the radius of the circle since all we know is the area of the circle.

2. Double the radius to find the diameter.

3. Find the circumference by $C=\pi d$

4. Write the ratio

$A_{circle}=\pi r^2$

$16\pi=\pi r^2$

Solving to find the radius we get:

16=r^2

4=r

So if the radius is 4 then the diameter is:

d=2(4)=8

Then the circumference is:

$C=8\pi$

The ratio of the diameter to the circumference is:

$\frac{d}{C}=\frac{8}{8\pi}=\frac{1}{\pi}$

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Example Question #1 : How To Find The Ratio Of Diameter And Circumference

The circumference of the base of a silo is $144\pi$ ft. What is the ratio of the silo's circumference to its diameter?

Possible Answers:

$\pi:1$

1:144

144:1

$144:\pi$

$1:\pi$

Correct answer:

$\pi:1$

Explanation:

Since the silo has base circumference of $144\pi$ , then according to the formula for the circumference of a circle:

$C=\pi d$

$144\pi=\pi d$

Solving for diameter:

144=d

So the diameter is 144 ft. Therefore the ratio of the circumference to the diameter would be:

$144\pi:144\rightarrow \pi:1$

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Example Question #2 : How To Find The Ratio Of Diameter And Circumference

The diameter of a certain circle is tripled. Compared to the circumference of the original circle, how many times as large is the circumference of the new circle?

Possible Answers:

$3\pi$

$9\pi$

Correct answer:

Explanation:

The easiest way to find our answer is to try actual values. Imagine we have a circle with a diameter of . Given the formula for circumference

$C=d\pi$

our circumference is simply $2\pi$ . Tripling the diameter gives a new diameter of and therefore a new circumference of $6\pi$ . We can then determine the ratio between the two circumferences.

$\frac{6\pi}{2\pi}=3$

Therefore, the new circumference is 3 times as large as the old.

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Example Question #371 : Circles

Find the ratio of the diameter to the circumference in a circle with radius r.

Possible Answers:

$2\pi{r}$

$\frac{1}{\pi}$

$\pi$

Correct answer:

$\frac{1}{\pi}$

Explanation:

To find a ratio, simply divide your two quantities. Remember,

D=2r

$C=2\pi{r}$

Thus,

$ratio=\frac{D}{C}=\frac{2r}{2\pi{r}}=\frac{1}{\pi}$

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Example Question #72 : Diameter

What is the circumference to diameter ratio of a circle with a diameter of 15?

Possible Answers:

3.14

4.75

3.75

Cannot be determined.

4.14

Correct answer:

3.14

Explanation:

First you must find the circumference of a circle with a diameter of 15 with the formula $C=\pi*D$ .

$C=\pi*15=47.1$

Since the ratio of C to D is represented by $\pi=\frac{C}{D}$ , all of the ratios of Circumference to Diameter should approximately equal $\pi$ .

$\frac{47.1}{15}=3.14$

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Example Question #372 : Basic Geometry

In the game of Sumo, both wrestlers are placed on the outer edge of the ring, on opposite sides of each other. If the wrestling ring is a perfect circle and has an area of $804.25\;ft^2$ , what would be the distance between both wrestlers?

Possible Answers:

$64\;ft$

$56\;ft$

$16\;ft$

$32\;ft$

$256\;ft$

Correct answer:

$32\;ft$

Explanation:

With the two wrestlers standing opposite each other on the edge of the ring, the distance between them would constitute the diameter of the circle. We can use the formula for circular area to find the diameter:

$\\area=\pi\cdot r^2\\ \\804.25\;ft^2=3.14159\cdot r^2\\ \\r^2=\frac{804.25\;ft^2}{3.14159}=256\;ft^2\\ \\radius=\sqrt{256\;ft^2}=16\;ft\\ \\diameter=2\cdot16\;ft=32\;ft$

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Example Question #372 : Plane Geometry

True or false: A circle with radius 1 has circumference less than 4.

Possible Answers:

False

True

Correct answer:

False

Explanation:

The circumference of a circle is equal to its radius multiplied by $2 \pi$ , so, if the radius of a circle is 1, its circumference is

$1 \times 2 \pi = 2\pi \approx 2 \cdot 3.14 \approx 6.28$

This is greater than 4.

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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #371 : Basic Geometry

Example Question #372 : Basic Geometry

Example Question #1 : Diameter And Chords

Example Question #1 : How To Find The Ratio Of Diameter And Circumference

Example Question #1 : How To Find The Ratio Of Diameter And Circumference

Example Question #2 : How To Find The Ratio Of Diameter And Circumference

Example Question #371 : Circles

Example Question #72 : Diameter

Example Question #372 : Basic Geometry

Example Question #372 : Plane Geometry

All Basic Geometry Resources

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