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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #321 : Plane Geometry

Find the diameter of a circle whose area is $\frac{1}{4}\pi$ .

Possible Answers:

$\frac{1}{2}$

$\frac{1}{4}$

Correct answer:

Explanation:

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$

Next, plug in the information given by the question.

$\frac{1}{4}\pi=\pi\times\text{radius}^2$

From this, we can see that we can solve for the radius.

$\text{radius}^2=\frac{1}{4}$

$\text{radius}=\sqrt{\frac{1}{4}}=\frac{1}{2}$

Now recall the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Plug in the value of the radius to find the diameter.

$\text{diameter}=2\times \frac{1}{2} = 1$

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Example Question #321 : Circles

Find the diameter of a circle whose area is $\frac{1}{16}\pi$ .

Possible Answers:

$\frac{1}{8}$

$\frac{1}{4}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$

Next, plug in the information given by the question.

$\frac{1}{16}\pi=\pi\times\text{radius}^2$

From this, we can see that we can solve for the radius.

$\text{radius}^2=\frac{1}{16}$

$\text{radius}=\sqrt{\frac{1}{16}}=\frac{1}{4}$

Now recall the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Plug in the value of the radius to find the diameter.

$\text{diameter}=2\times \frac{1}{4} = \frac{1}{2}$

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Example Question #321 : Circles

Find the diameter of a circle whose area is $484\pi$ .

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$

Next, plug in the information given by the question.

$484\pi=\pi\times\text{radius}^2$

From this, we can see that we can solve for the radius.

$\text{radius}^2=484$

$\text{radius}=\sqrt{484}=22$

Now recall the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Plug in the value of the radius to find the diameter.

$\text{diameter}=2\times 22 = 44$

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Example Question #12 : How To Find The Length Of The Diameter

Find the diameter of a circle whose area is $3025\pi$ .

Possible Answers:

110

220

Correct answer:

110

Explanation:

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$

Next, plug in the information given by the question.

$3025\pi=\pi\times\text{radius}^2$

From this, we can see that we can solve for the radius.

$\text{radius}^2=3025$

$\text{radius}=\sqrt{3025}=55$

Now recall the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Plug in the value of the radius to find the diameter.

$\text{diameter}=2\times 55 = 110$

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Example Question #19 : How To Find The Length Of The Diameter

Find the diameter of a circle whose area is $529\pi$ .

Possible Answers:

Correct answer:

Explanation:

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$

Next, plug in the information given by the question.

$529\pi=\pi\times\text{radius}^2$

From this, we can see that we can solve for the radius.

$\text{radius}^2=529$

$\text{radius}=\sqrt{529}=23$

Now recall the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Plug in the value of the radius to find the diameter.

$\text{diameter}=2\times 23 = 46$

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Example Question #322 : Plane Geometry

Find the diameter of a circle whose area is $1156\pi$ .

Possible Answers:

136

Correct answer:

Explanation:

Recall how to find the area of a circle:

$\text{Area}=\pi\times\text{radius}^2$

Next, plug in the information given by the question.

$1156\pi=\pi\times\text{radius}^2$

From this, we can see that we can solve for the radius.

$\text{radius}^2=1156$

$\text{radius}=\sqrt{1156}=34$

Now recall the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Plug in the value of the radius to find the diameter.

$\text{diameter}=2\times 34 = 68$

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Example Question #21 : Diameter

Find the diameter of a circle that has a circumference of .

Possible Answers:

$\frac{6}{\pi}$

$\frac{12}{\pi}$

Correct answer:

$\frac{12}{\pi}$

Explanation:

Recall how to find the circumference of a circle:

$\text{Circumference}=\text{diameter}\times\pi$

If we divide both sides of the equation by $\pi$ , then we can write the following equation:

$\text{Diameter}=\frac{\text{Circumference}}{\pi}$

We can substitute in the given information to find the diameter of the circle in the question.

$\text{Diameter}=\frac{12}{\pi}$

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Example Question #321 : Plane Geometry

Find the diameter of a circle that has a circumference of 100 .

Possible Answers:

100

$\frac{50}{\pi}$

$\frac{100}{\pi}$

$\frac{200}{\pi}$

Correct answer:

$\frac{100}{\pi}$

Explanation:

Recall how to find the circumference of a circle:

$\text{Circumference}=\text{diameter}\times\pi$

If we divide both sides of the equation by $\pi$ , then we can write the following equation:

$\text{Diameter}=\frac{\text{Circumference}}{\pi}$

We can substitute in the given information to find the diameter of the circle in the question.

$\text{Diameter}=\frac{100}{\pi}$

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Example Question #24 : Diameter

Find the diameter of a circle that has a circumference of $14\pi$ .

Possible Answers:

$\pi$

Correct answer:

Explanation:

Recall how to find the circumference of a circle:

$\text{Circumference}=\text{diameter}\times\pi$

If we divide both sides of the equation by $\pi$ , then we can write the following equation:

$\text{Diameter}=\frac{\text{Circumference}}{\pi}$

We can substitute in the given information to find the diameter of the circle in the question.

$\text{Diameter}=\frac{14\pi}{\pi}$

Simplify.

$\text{Diameter}=14$

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Example Question #321 : Circles

Find the diameter of a circle that has a circumference of $10\pi$ .

Possible Answers:

Correct answer:

Explanation:

Recall how to find the circumference of a circle:

$\text{Circumference}=\text{diameter}\times\pi$

If we divide both sides of the equation by $\pi$ , then we can write the following equation:

$\text{Diameter}=\frac{\text{Circumference}}{\pi}$

We can substitute in the given information to find the diameter of the circle in the question.

$\text{Diameter}=\frac{10\pi}{\pi}$

Simplify.

$\text{Diameter}=10$

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #321 : Plane Geometry

Example Question #321 : Circles

Example Question #321 : Circles

Example Question #12 : How To Find The Length Of The Diameter

Example Question #19 : How To Find The Length Of The Diameter

Example Question #322 : Plane Geometry

Example Question #21 : Diameter

Example Question #321 : Plane Geometry

Example Question #24 : Diameter

Example Question #321 : Circles

All Basic Geometry Resources

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