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Basic Geometry : How to find circumference

Study concepts, example questions & explanations for Basic Geometry

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9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #251 : Radius

The rectangle and the circle share the same center, $\displaystyle C$ . Find the circumference of the circle.

Possible Answers:

$4\sqrt{10}\pi$ $\displaystyle 4\sqrt{10}\pi$

$6\sqrt{10}\pi$ $\displaystyle 6\sqrt{10}\pi$

$3\sqrt{10}\pi$ $\displaystyle 3\sqrt{10}\pi$

$5\sqrt{10}\pi$ $\displaystyle 5\sqrt{10}\pi$

Correct answer:

$4\sqrt{10}\pi$ $\displaystyle 4\sqrt{10}\pi$

Explanation:

Notice that the diagonal of the rectangle is also the diameter of the circle.

Use the Pythagorean theorem to find the length of the diagonal.

$\text{length}^2+\text{width}^2=\text{diagonal}^2$ $\displaystyle \text{length}^2+\text{width}^2=\text{diagonal}^2$

$\text{diagonal}=\sqrt{\text{length}^2+\text{width}^2}$ $\displaystyle \text{diagonal}=\sqrt{\text{length}^2+\text{width}^2}$

Substitute in the values of the length and the width to find the length of the diagonal.

$\text{diagonal}=\sqrt{4^2+12^2}$ $\displaystyle \text{diagonal}=\sqrt{4^2+12^2}$

Simplify.

$\text{diagonal}=\sqrt{160}$ $\displaystyle \text{diagonal}=\sqrt{160}$

Reduce.

$\text{diagonal}=4\sqrt{10}$ $\displaystyle \text{diagonal}=4\sqrt{10}$

Now, recall the relationship between the diagonal and the diameter.

$\text{diagonal}=\text{diameter}=4\sqrt{10}$ $\displaystyle \text{diagonal}=\text{diameter}=4\sqrt{10}$

Recall how to find the circumference of a circle:

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

Substitute in the value of the diameter to find the circumference.

$\text{Circumference}=4\sqrt{10}\pi$ $\displaystyle \text{Circumference}=4\sqrt{10}\pi$

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Example Question #252 : Plane Geometry

The rectangle and the circle share the same center, $\displaystyle C$ . Find the circumference of the circle.

Possible Answers:

$4\sqrt{19}\pi$ $\displaystyle 4\sqrt{19}\pi$

$4\sqrt{17}\pi$ $\displaystyle 4\sqrt{17}\pi$

$4\sqrt{15}\pi$ $\displaystyle 4\sqrt{15}\pi$

$4\sqrt{14}\pi$ $\displaystyle 4\sqrt{14}\pi$

Correct answer:

$4\sqrt{17}\pi$ $\displaystyle 4\sqrt{17}\pi$

Explanation:

Notice that the diagonal of the rectangle is also the diameter of the circle.

Use the Pythagorean theorem to find the length of the diagonal.

$\text{length}^2+\text{width}^2=\text{diagonal}^2$ $\displaystyle \text{length}^2+\text{width}^2=\text{diagonal}^2$

$\text{diagonal}=\sqrt{\text{length}^2+\text{width}^2}$ $\displaystyle \text{diagonal}=\sqrt{\text{length}^2+\text{width}^2}$

Substitute in the values of the length and the width to find the length of the diagonal.

$\text{diagonal}=\sqrt{4^2+16^2}$ $\displaystyle \text{diagonal}=\sqrt{4^2+16^2}$

Simplify.

$\text{diagonal}=\sqrt{272}$ $\displaystyle \text{diagonal}=\sqrt{272}$

Reduce.

$\text{diagonal}=4\sqrt{17}$ $\displaystyle \text{diagonal}=4\sqrt{17}$

Now, recall the relationship between the diagonal and the diameter.

$\text{diagonal}=\text{diameter}=4\sqrt{17}$ $\displaystyle \text{diagonal}=\text{diameter}=4\sqrt{17}$

Recall how to find the circumference of a circle:

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

Substitute in the value of the diameter to find the circumference.

$\text{Circumference}=4\sqrt{17}\pi$ $\displaystyle \text{Circumference}=4\sqrt{17}\pi$

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Example Question #61 : How To Find Circumference

Find the circumference of a circle given radius $\displaystyle 4x$ .

Possible Answers:

$8x\pi$ $\displaystyle 8x\pi$

$\displaystyle 4x$

$\displaystyle 8x$

$4x\pi$ $\displaystyle 4x\pi$

Correct answer:

$8x\pi$ $\displaystyle 8x\pi$

Explanation:

To solve, simply use the formula for circumference. Thus,

$C=2\pi{r}=2*\pi*4x=8x\pi$ $\displaystyle C=2\pi{r}=2*\pi*4x=8x\pi$

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Example Question #62 : How To Find Circumference

If a rectangle with a diagonal of $14\sqrt7$ $\displaystyle 14\sqrt7$ is inscribed in a circle, what is the circumference of the circle?

Possible Answers:

$28\sqrt7\pi$ $\displaystyle 28\sqrt7\pi$

$196\pi$ $\displaystyle 196\pi$

$32\pi$ $\displaystyle 32\pi$

$14\sqrt7\pi$ $\displaystyle 14\sqrt7\pi$

Correct answer:

$14\sqrt7\pi$ $\displaystyle 14\sqrt7\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=14\sqrt7$ $\displaystyle \text{Diameter}=\text{Diagonal}=14\sqrt7$

Now, recall how to find the circumference of a circle.

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

Substitute in the given diameter to find the circumference.

$\text{Circumference}=14\sqrt7\pi$ $\displaystyle \text{Circumference}=14\sqrt7\pi$

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Example Question #63 : How To Find Circumference

If a rectangle with a diagonal of $\displaystyle 12$ is inscribed in a circle, what is the circumference of the circle?

Possible Answers:

$6\pi$ $\displaystyle 6\pi$

$144\pi$ $\displaystyle 144\pi$

$12\pi$ $\displaystyle 12\pi$

$4\pi$ $\displaystyle 4\pi$

Correct answer:

$12\pi$ $\displaystyle 12\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=12$ $\displaystyle \text{Diameter}=\text{Diagonal}=12$

Now, recall how to find the circumference of a circle.

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

Substitute in the given diameter to find the circumference.

$\text{Circumference}=12\pi$ $\displaystyle \text{Circumference}=12\pi$

Report an Error

Example Question #62 : How To Find Circumference

If a rectangle with a diagonal of $2\sqrt5$ $\displaystyle 2\sqrt5$ is inscribed in a circle, what is the circumference of the circle?

Possible Answers:

$4\sqrt{5}\pi$ $\displaystyle 4\sqrt{5}\pi$

$8\sqrt5\pi$ $\displaystyle 8\sqrt5\pi$

$50\pi$ $\displaystyle 50\pi$

$2\sqrt5\pi$ $\displaystyle 2\sqrt5\pi$

Correct answer:

$2\sqrt5\pi$ $\displaystyle 2\sqrt5\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=2\sqrt5$ $\displaystyle \text{Diameter}=\text{Diagonal}=2\sqrt5$

Now, recall how to find the circumference of a circle.

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

Substitute in the given diameter to find the circumference.

$\text{Circumference}=2\sqrt5\pi$ $\displaystyle \text{Circumference}=2\sqrt5\pi$

Report an Error

Example Question #65 : How To Find Circumference

If a rectangle with a diagonal of $4\sqrt{10}$ $\displaystyle 4\sqrt{10}$ is inscribed in a circle, what is the circumference of the circle?

Possible Answers:

$4\sqrt{10}\pi$ $\displaystyle 4\sqrt{10}\pi$

$160\pi$ $\displaystyle 160\pi$

$80\pi$ $\displaystyle 80\pi$

$8\sqrt{10}\pi$ $\displaystyle 8\sqrt{10}\pi$

Correct answer:

$4\sqrt{10}\pi$ $\displaystyle 4\sqrt{10}\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=4\sqrt{10}$ $\displaystyle \text{Diameter}=\text{Diagonal}=4\sqrt{10}$

Now, recall how to find the circumference of a circle.

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

Substitute in the given diameter to find the circumference.

$\text{Circumference}=4\sqrt{10}\pi$ $\displaystyle \text{Circumference}=4\sqrt{10}\pi$

Report an Error

Example Question #252 : Basic Geometry

If a rectangle with a diagonal of $15\sqrt3$ $\displaystyle 15\sqrt3$ is inscribed in a circle, what is the circumference of the circle?

Possible Answers:

$30\sqrt3\pi$ $\displaystyle 30\sqrt3\pi$

$250\pi$ $\displaystyle 250\pi$

$15\sqrt3\pi$ $\displaystyle 15\sqrt3\pi$

$15\pi$ $\displaystyle 15\pi$

Correct answer:

$15\sqrt3\pi$ $\displaystyle 15\sqrt3\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=15\sqrt3$ $\displaystyle \text{Diameter}=\text{Diagonal}=15\sqrt3$

Now, recall how to find the circumference of a circle.

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

Substitute in the given diameter to find the circumference.

$\text{Circumference}=15\sqrt3\pi$ $\displaystyle \text{Circumference}=15\sqrt3\pi$

Report an Error

Example Question #62 : How To Find Circumference

If a rectangle with a diagonal of 224 $\displaystyle 224$ is inscribed in a circle, what is the circumference of the circle?

Possible Answers:

$112\pi$ $\displaystyle 112\pi$

$24\sqrt{3}\pi$ $\displaystyle 24\sqrt{3}\pi$

$336\pi$ $\displaystyle 336\pi$

$224\pi$ $\displaystyle 224\pi$

Correct answer:

$224\pi$ $\displaystyle 224\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=224$ $\displaystyle \text{Diameter}=\text{Diagonal}=224$

Now, recall how to find the circumference of a circle.

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

Substitute in the given diameter to find the circumference.

$\text{Circumference}=224\pi$ $\displaystyle \text{Circumference}=224\pi$

Report an Error

Example Question #261 : Basic Geometry

If a rectangle with a diagonal of $\displaystyle 19$ is inscribed in a circle, what is the circumference of the circle?

Possible Answers:

$19\pi$ $\displaystyle 19\pi$

$381\pi$ $\displaystyle 381\pi$

$38\pi$ $\displaystyle 38\pi$

$\frac{19}{2}\pi$ $\displaystyle \frac{19}{2}\pi$

Correct answer:

$19\pi$ $\displaystyle 19\pi$

Explanation:

Notice that the diagonal of the rectangle is the same as the diameter of the circle.

$\text{Diameter}=\text{Diagonal}=19$ $\displaystyle \text{Diameter}=\text{Diagonal}=19$

Now, recall how to find the circumference of a circle.

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

Substitute in the given diameter to find the circumference.

$\text{Circumference}=19\pi$ $\displaystyle \text{Circumference}=19\pi$

Report an Error

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Basic Geometry : How to find circumference

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #251 : Radius

Example Question #252 : Plane Geometry

Example Question #61 : How To Find Circumference

Example Question #62 : How To Find Circumference

Example Question #63 : How To Find Circumference

Example Question #62 : How To Find Circumference

Example Question #65 : How To Find Circumference

Example Question #252 : Basic Geometry

Example Question #62 : How To Find Circumference

Example Question #261 : Basic Geometry

All Basic Geometry Resources

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