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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #251 : Circles

The circle and the rectangle share a center, . Find the circumference of the circle.

Possible Answers:

$3\sqrt{7}\pi$

$10\sqrt{3}\pi$

$4\sqrt{5}\pi$

$2\sqrt{10}\pi$

Correct answer:

$4\sqrt{5}\pi$

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.

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

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

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

$\text{diagonal}=\sqrt{4^2+8^2}$

Simplify.

$\text{diagonal}=\sqrt{80}$

Reduce.

$\text{diagonal}=4\sqrt{5}$

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

$\text{diagonal}=\text{diameter}=4\sqrt{5}$

Recall how to find the circumference of a circle:

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

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

$\text{Circumference}=4\sqrt{5}\pi$

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Example Question #251 : Radius

The rectangle and the circle share the same center, . Find the circumference of the circle.

Possible Answers:

$4\sqrt{10}\pi$

$6\sqrt{10}\pi$

$3\sqrt{10}\pi$

$5\sqrt{10}\pi$

Correct answer:

$4\sqrt{10}\pi$

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.

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

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

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

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

Simplify.

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

Reduce.

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

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

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

Recall how to find the circumference of a circle:

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

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

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

Report an Error

Example Question #252 : Plane Geometry

The rectangle and the circle share the same center, . Find the circumference of the circle.

Possible Answers:

$4\sqrt{19}\pi$

$4\sqrt{17}\pi$

$4\sqrt{15}\pi$

$4\sqrt{14}\pi$

Correct answer:

$4\sqrt{17}\pi$

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.

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

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

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

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

Simplify.

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

Reduce.

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

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

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

Recall how to find the circumference of a circle:

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

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

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

Report an Error

Example Question #251 : Circles

Find the circumference of a circle given radius .

Possible Answers:

$4x\pi$

$8x\pi$

Correct answer:

$8x\pi$

Explanation:

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

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

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Example Question #62 : How To Find Circumference

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

Possible Answers:

$28\sqrt7\pi$

$196\pi$

$32\pi$

$14\sqrt7\pi$

Correct answer:

$14\sqrt7\pi$

Explanation:

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

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

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

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

Substitute in the given diameter to find the circumference.

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

Report an Error

Example Question #254 : Plane Geometry

If a rectangle with a diagonal of is inscribed in a circle, what is the circumference of the circle?

Possible Answers:

$12\pi$

$4\pi$

$6\pi$

$144\pi$

Correct answer:

$12\pi$

Explanation:

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

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

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

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

Substitute in the given diameter to find the circumference.

$\text{Circumference}=12\pi$

Report an Error

Example Question #254 : Circles

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

Possible Answers:

$50\pi$

$2\sqrt5\pi$

$8\sqrt5\pi$

$4\sqrt{5}\pi$

Correct answer:

$2\sqrt5\pi$

Explanation:

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

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

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

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

Substitute in the given diameter to find the circumference.

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

Report an Error

Example Question #253 : Circles

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

Possible Answers:

$80\pi$

$8\sqrt{10}\pi$

$160\pi$

$4\sqrt{10}\pi$

Correct answer:

$4\sqrt{10}\pi$

Explanation:

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

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

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

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

Substitute in the given diameter to find the circumference.

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

Report an Error

Example Question #256 : Circles

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

Possible Answers:

$15\sqrt3\pi$

$250\pi$

$15\pi$

$30\sqrt3\pi$

Correct answer:

$15\sqrt3\pi$

Explanation:

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

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

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

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

Substitute in the given diameter to find the circumference.

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

Report an Error

Example Question #252 : Circles

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

Possible Answers:

$112\pi$

$224\pi$

$336\pi$

$24\sqrt{3}\pi$

Correct answer:

$224\pi$

Explanation:

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

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

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

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

Substitute in the given diameter to find the circumference.

$\text{Circumference}=224\pi$

Report an Error

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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #251 : Circles

Example Question #251 : Radius

Example Question #252 : Plane Geometry

Example Question #251 : Circles

Example Question #62 : How To Find Circumference

Example Question #254 : Plane Geometry

Example Question #254 : Circles

Example Question #253 : Circles

Example Question #256 : Circles

Example Question #252 : Circles

All Basic Geometry Resources

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