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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #91 : How To Find Circumference

Find the circumference of the circle if the lengths of the legs of the inscribed isosceles triangle are .

Possible Answers:

$3\sqrt2\pi$

$9\sqrt2\pi$

$\sqrt3\pi$

$3\pi$

Correct answer:

$3\sqrt2\pi$

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.

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

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

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

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

$\text{Hypotenuse}=3\sqrt2$

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

$\text{Hypotenuse}=\text{Diameter}=3\sqrt2$

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

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

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

$\text{Circumference}=3\sqrt2\pi$

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Example Question #291 : Circles

Find the circumference of the circle if the lengths of the legs of the inscribed isosceles triangle are .

Possible Answers:

$2\pi$

$2\sqrt2\pi$

$8\sqrt2\pi$

$\sqrt2\pi$

Correct answer:

$2\sqrt2\pi$

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.

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

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

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

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

$\text{Hypotenuse}=2\sqrt2$

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

$\text{Hypotenuse}=\text{Diameter}=2\sqrt2$

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

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

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

$\text{Circumference}=2\sqrt2\pi$

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Example Question #292 : Circles

Find the circumference of a circle whose radius is 5.

Possible Answers:

$10\pi$

$25\pi$

Correct answer:

$10\pi$

Explanation:

The circumference of a circle is the length of the outside curved line which incloses the circle.

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

Thus,

r=5

$c=2\pi{r}=2*\pi*5=10\pi$

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Example Question #293 : Circles

Find the circumference of a circle given the radius is 7.

Possible Answers:

$14\pi$

$49\pi$

Correct answer:

$14\pi$

Explanation:

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

$C=2\pi{r}=2*\pi*7=14\pi$

Another way to similarly solve this problem is to remember that circumference is just pi times the diameter. To find the diameter, remember "di" means two, thus two radii. So, if you multiply the radius by 2, then you have the diameter. Then, just multiply by pi.

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Example Question #101 : How To Find Circumference

A circle has a radius of 3.5 cm . What is the circumference of the circle?

Possible Answers:

$12.25\pi cm$

$3.5\pi cm$

$49\pi cm$

$\pi cm$

$7\pi cm$

Correct answer:

$7\pi cm$

Explanation:

The formula to find the circumference of a cirlce using the radius is:

$C=2\pi r$

The radius is 3.5 cm , so we plug that into the formula:

$C=2\pi (3.5)$

$C=7\pi cm$

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Example Question #294 : Circles

What is the circumference of a circle with a radius of $5.2\textup{ in}$ ?

Possible Answers:

$16.3\textup{ in}$

$10.4\textup{ in}$

$32.7\textup{ in}$

$22.8\textup{ in}$

$49.3\textup{ in}$

(Round your answer to the nearest tenth.)

Correct answer:

$32.7\textup{ in}$

Explanation:

The circumference is given by the formula:

$C=2\pi r$

where is the radius.

$2\pi (5.2)=32.7\ in$

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Example Question #102 : How To Find Circumference

A vinyl record uncovered from your grandfather's attic is circular in shape and has a diameter of {10}'' . What is the circumferance of the record rounded to the nearest tenth?

Possible Answers:

31.4{}''

{15.7}''

{23.7}''

{30.2}''

{62.8}''

Correct answer:

31.4{}''

Explanation:

To find the circumference, we want to use the formula for calculating circumference:

$\\circ.=\pi\cdot d\\circ.=3.14159\cdot10{}''\\circ.\approx31.4{}''$

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Example Question #102 : How To Find Circumference

A {12}'' diameter vinyl record plays music by rotating the circular disc along a fine-point needle. The attached figure shows the location of the needle in respect to the spinning record. If the needle is placed {3}'' from the outer edge of the record, what would be the "circumference" of one full rotation?
Varsity record

Possible Answers:

{18.8}''

{28.3}''

{15.7}''

{28.9}''

{25.5}''

Correct answer:

{18.8}''

Explanation:

Since the vinyl record has a diameter of {12}'' , the radius is {6}'' . If the needle is placed {3}'' from the edge of the disc, the circumference of that full rotation is calculated from a radius of {6}''-{3}'' , or a {3}'' radius. We can then find the circumference as such:

$\\circ.=\pi\cdot\2\cdot{3}''\\circ.=3.14159\cdot\2\cdot{3}''\\circ.\approx{18.8}''$

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Example Question #103 : How To Find Circumference

If the area of a circle is $25 \pi in^2$ , what is the measure of its circumference?

Possible Answers:

$10 \pi in$

$5 \pi in$

$25 \pi in$

$50 \pi in$

Correct answer:

$10 \pi in$

Explanation:

The area of a circle is found by using the formula $area = \pi r^2$ . To figure out the radius of the circle, plug in the area given:

$25 \pi = \pi r^ 2$ divide both sides by pi

25 = r^2 take the square root of both sides

5 = r

Now we can plug that into the formula for the circumference, $C = 2 \pi r$ . Here, $C = 2 \pi \cdot 5 = 10 \pi$

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Example Question #108 : How To Find Circumference

What is the circumference of a circle with diameter of 60cm?

Possible Answers:

$900\pi cm$

$300\pi cm$

$3600\pi cm$

$30\pi cm$

$60\pi cm$

Correct answer:

$60\pi cm$

Explanation:

The circumference formula for a circle ism

$C=2\pi r$

The Radius of the circle is half the diameter, in this case 30.

Now substitute the radius into the circumference formula to solve.

$C=2\pi30cm$

$C=60\pi cm$

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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #91 : How To Find Circumference

Example Question #291 : Circles

Example Question #292 : Circles

Example Question #293 : Circles

Example Question #101 : How To Find Circumference

Example Question #294 : Circles

Example Question #102 : How To Find Circumference

Example Question #102 : How To Find Circumference

Example Question #103 : How To Find Circumference

Example Question #108 : How To Find Circumference

All Basic Geometry Resources

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