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Basic Geometry : Diameter

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Example Questions

Example Question #362 : Circles

The area of a circle is $196\pi$ inches^2 . What is the diameter?

Possible Answers:

$32\ in$

$14\ in$

$16\ in$

$28\ in$

$22\ in$

Correct answer:

$28\ in$

Explanation:

To find the diameter, we must first find the radius using the formula to find a circle's area.

$\pi r^2=area$

We have the area, so we have to work backwards.

$\pi r^2=196\pi$

Divide both sides by $\pi$

r^2=196

Take the square root of both sides.

$\sqrt{r^2}=\sqrt{196}$

r=14 inches

Now, since you have the radius, you have to double it to get the diameter.

diameter = 28 inches

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Example Question #61 : Diameter

The area of a circle is $81 \pi \enspace un^2$ . What is the diameter?

Possible Answers:

4.5 un

81 un

9 un

18 un

Correct answer:

18 un

Explanation:

The area of a circle is $\pi r^2$ , which means that in this circle, the radius squared is 81. The square root of 81 is 9, which means that the radius is 9. The diameter is just twice the length of the radius, so in this case 9 times 2, which is 18.

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Example Question #62 : Diameter

The area of a circle is $25 \pi \enspace in^2$ . What is the length of its diameter?

Possible Answers:

2.5 in

25 in

5 in

50 in

10 in

Correct answer:

10 in

Explanation:

The area of a circle is $\pi r^2$ . In this case, r ^2 = 25 . Taking the square root, the radius has a length of 5. To find the diameter, multiply by 2. Two times five is 10, so the diameter has a length of 10.

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Example Question #365 : Circles

True or false: A circle with radius 20 has diameter 10.

Possible Answers:

True

False

Correct answer:

False

Explanation:

The diameter of a circle is twice its radius (not the other way around), so a circle with radius 20 has diameter $2 \times 20 = 40$ .

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Example Question #364 : Basic Geometry

True or false: A circle with radius 500 centimeters has diameter one meter.

Possible Answers:

False

True

Correct answer:

False

Explanation:

The diameter of a circle is twice that of the radius, so the diameter of a circle with radius 500 centimeters is $500 \textrm{ cm} \times 2 = 1,000 \textrm{ cm}$ . However, one meter is equal to 100 centimeters, so the statement is false.

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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 : How To Find The Ratio Of Diameter And Circumference

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:

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

$\frac{1}{\pi}$

$\frac{\pi}{8}$

$\frac{\pi}{1}$

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

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 #2 : 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:

1:144

$144:\pi$

144:1

$\pi:1$

$1:\pi$

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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Basic Geometry : Diameter

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #362 : Circles

Example Question #61 : Diameter

Example Question #62 : Diameter

Example Question #365 : Circles

Example Question #364 : Basic Geometry

Example Question #371 : Basic Geometry

Example Question #372 : Basic Geometry

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

All Basic Geometry Resources

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