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Basic Geometry : Radius

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Example Questions

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.

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

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Example Question #261 : Radius

If a rectangle with a diagonal of $\frac{4}{5}$ $\displaystyle \frac{4}{5}$ is inscribed in a circle, what is the circumference of the circle?

Possible Answers:

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

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

$\frac{2\sqrt5}{5}\pi$ $\displaystyle \frac{2\sqrt5}{5}\pi$

$\frac{16}{25}\pi$ $\displaystyle \frac{16}{25}\pi$

Correct answer:

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

Explanation:

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

$\text{Diameter}=\text{Diagonal}=\frac{4}{5}$ $\displaystyle \text{Diameter}=\text{Diagonal}=\frac{4}{5}$

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.

$\text{Circumference}=\frac{4}{5}\pi$ $\displaystyle \text{Circumference}=\frac{4}{5}\pi$

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Example Question #263 : Basic Geometry

If a rectangle with a diagonal of $4\sqrt3$ $\displaystyle 4\sqrt3$ is inscribed in a circle, what is the circumference of the circle?

Possible Answers:

$16\sqrt3\pi$ $\displaystyle 16\sqrt3\pi$

$4\sqrt3\pi$ $\displaystyle 4\sqrt3\pi$

$8\sqrt3\pi$ $\displaystyle 8\sqrt3\pi$

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

Correct answer:

$4\sqrt3\pi$ $\displaystyle 4\sqrt3\pi$

Explanation:

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

$\text{Diameter}=\text{Diagonal}=4\sqrt3$ $\displaystyle \text{Diameter}=\text{Diagonal}=4\sqrt3$

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.

$\text{Circumference}=4\sqrt3\pi$ $\displaystyle \text{Circumference}=4\sqrt3\pi$

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Example Question #264 : Basic Geometry

If a rectangle with a diagonal of 201 $\displaystyle 201$ is inscribed in a circle, what is the circumference of the circle?

Possible Answers:

$402\pi$ $\displaystyle 402\pi$

$201\pi$ $\displaystyle 201\pi$

$\frac{201}{2}\pi$ $\displaystyle \frac{201}{2}\pi$

201 $\displaystyle 201$

Correct answer:

$201\pi$ $\displaystyle 201\pi$

Explanation:

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

$\text{Diameter}=\text{Diagonal}=201$ $\displaystyle \text{Diameter}=\text{Diagonal}=201$

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.

$\text{Circumference}=201\pi$ $\displaystyle \text{Circumference}=201\pi$

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Example Question #261 : Basic Geometry

If a rectangle with a diagonal of $18\sqrt{7}$ $\displaystyle 18\sqrt{7}$ is inscribed in a circle, what is the circumference of the circle?

Possible Answers:

$12\sqrt7\pi$ $\displaystyle 12\sqrt7\pi$

$9\sqrt7\pi$ $\displaystyle 9\sqrt7\pi$

$36\sqrt7\pi$ $\displaystyle 36\sqrt7\pi$

$18\sqrt7\pi$ $\displaystyle 18\sqrt7\pi$

Correct answer:

$18\sqrt7\pi$ $\displaystyle 18\sqrt7\pi$

Explanation:

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

$\text{Diameter}=\text{Diagonal}=18\sqrt7$ $\displaystyle \text{Diameter}=\text{Diagonal}=18\sqrt7$

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.

$\text{Circumference}=18\sqrt7\pi$ $\displaystyle \text{Circumference}=18\sqrt7\pi$

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Example Question #266 : Basic Geometry

If a rectangle with a diagonal of $\frac{9}{8}$ $\displaystyle \frac{9}{8}$ is inscribed in a circle, what is the circumference of the circle?

Possible Answers:

$\frac{4}{3}\pi$ $\displaystyle \frac{4}{3}\pi$

$\frac{9}{8}\pi$ $\displaystyle \frac{9}{8}\pi$

$3\sqrt2\pi$ $\displaystyle 3\sqrt2\pi$

$\frac{8}{9}\pi$ $\displaystyle \frac{8}{9}\pi$

Correct answer:

$\frac{9}{8}\pi$ $\displaystyle \frac{9}{8}\pi$

Explanation:

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

$\text{Diameter}=\text{Diagonal}=\frac{8}{9}$ $\displaystyle \text{Diameter}=\text{Diagonal}=\frac{8}{9}$

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.

$\text{Circumference}=\frac{8}{9}\pi$ $\displaystyle \text{Circumference}=\frac{8}{9}\pi$

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Example Question #261 : Circles

Given that the radius of a circle is 20m $\displaystyle 20m$, solve for the circumference.

Possible Answers:

72.6 m $\displaystyle 72.6 m$

103.5 m $\displaystyle 103.5 m$

125.7 m $\displaystyle 125.7 m$

123.4 m $\displaystyle 123.4 m$

40 m $\displaystyle 40 m$

Correct answer:

125.7 m $\displaystyle 125.7 m$

Explanation:

The circumference of a circle is found by using the following formula:

$C=2 (\pi) (r)$ $\displaystyle C=2 (\pi) (r)$Plug in the radius from the given information, and you get this:

$C = 2 \pi (20)$ $\displaystyle C = 2 \pi (20)$

$\displaystyle C = 125.7 m$

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Example Question #262 : Basic Geometry

Find the circumference of a circle given the radius is 3.

Possible Answers:

$9\pi$ $\displaystyle 9\pi$

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

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

$18\pi$ $\displaystyle 18\pi$

Correct answer:

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

Explanation:

To solve, simply use the formula for the circumference of a circle.

Given that the radius is 3, substitute 3 in for the r in the circumference formula below.

Thus,

$\\C=2\pi{r}\\C=2*\pi*3\\C=6\pi$ $\displaystyle \\C=2\pi{r}\\C=2*\pi*3\\C=6\pi$.

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Example Question #269 : Basic Geometry

Find the circumference of the circle if the lengths of the legs of the inscribed isosceles triangle are $2\sqrt2$ $\displaystyle 2\sqrt2$.

Possible Answers:

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

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

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

$16\pi$ $\displaystyle 16\pi$

Correct answer:

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

Explanation:

Notice that the hypotenuse of the triangle in the figure is also the diameter of the circle.

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

$\text{Hypotenuse}^2=\text{leg}^2+\text{leg}^2$ $\displaystyle \text{Hypotenuse}^2=\text{leg}^2+\text{leg}^2$

$\text{Hypotenuse}^2=2(\text{leg}^2)$ $\displaystyle \text{Hypotenuse}^2=2(\text{leg}^2)$

$\text{Hypotenuse}=\sqrt{2(\text{leg}^2)}=\text{leg}\sqrt2$ $\displaystyle \text{Hypotenuse}=\sqrt{2(\text{leg}^2)}=\text{leg}\sqrt2$

Substitute in the length of triangle’s legs to find the missing length of the hypotenuse.

$\text{Hypotenuse}=2\sqrt2(\sqrt2)$ $\displaystyle \text{Hypotenuse}=2\sqrt2(\sqrt2)$

Simplify.

$\text{Hypotenuse}=4$ $\displaystyle \text{Hypotenuse}=4$

Now, recall that the hypotenuse of the triangle and the diameter of the circle are the same:

$\text{Hypotenuse}=\text{Diameter}=4$ $\displaystyle \text{Hypotenuse}=\text{Diameter}=4$

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 value for the diameter to find the circumference of the circle.

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

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Example Question #270 : Basic Geometry

Find the circumference of the circle if the lengths of the legs of the inscribed isosceles triangle are $3\sqrt2$ $\displaystyle 3\sqrt2$.

Possible Answers:

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

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

$18\pi$ $\displaystyle 18\pi$

$3\pi$ $\displaystyle 3\pi$

Correct answer:

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

Explanation:

Notice that the hypotenuse of the triangle in the figure is also the diameter of the circle.

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

$\text{Hypotenuse}^2=\text{leg}^2+\text{leg}^2$ $\displaystyle \text{Hypotenuse}^2=\text{leg}^2+\text{leg}^2$

$\text{Hypotenuse}^2=2(\text{leg}^2)$ $\displaystyle \text{Hypotenuse}^2=2(\text{leg}^2)$

$\text{Hypotenuse}=\sqrt{2(\text{leg}^2)}=\text{leg}\sqrt2$ $\displaystyle \text{Hypotenuse}=\sqrt{2(\text{leg}^2)}=\text{leg}\sqrt2$

Substitute in the length of triangle’s legs to find the missing length of the hypotenuse.

$\text{Hypotenuse}=3\sqrt2(\sqrt2)$ $\displaystyle \text{Hypotenuse}=3\sqrt2(\sqrt2)$

Simplify.

$\text{Hypotenuse}=6$ $\displaystyle \text{Hypotenuse}=6$

Now, recall that the hypotenuse of the triangle and the diameter of the circle are the same:

$\text{Hypotenuse}=\text{Diameter}=6$ $\displaystyle \text{Hypotenuse}=\text{Diameter}=6$

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 value for the diameter to find the circumference of the circle.

$\text{Circumference}=6\pi$ $\displaystyle \text{Circumference}=6\pi$

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Basic Geometry : Radius

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #261 : Basic Geometry

Example Question #261 : Radius

Example Question #263 : Basic Geometry

Example Question #264 : Basic Geometry

Example Question #261 : Basic Geometry

Example Question #266 : Basic Geometry

Example Question #261 : Circles

Example Question #262 : Basic Geometry

Example Question #269 : Basic Geometry

Example Question #270 : Basic Geometry

All Basic Geometry Resources

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