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Basic Geometry : Circles

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 #45 : Radius

A car tire has a radius of 18 inches. When the tire has made 200 revolutions, how far has the car gone in feet?

Possible Answers:

300π

3600π

600π

500π

Correct answer:

600π

Explanation:

If the radius is 18 inches, the diameter is 3 feet. The circumference of the tire is therefore 3π by C=d(π). After 200 revolutions, the tire and car have gone 3π x 200 = 600π feet.

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Example Question #46 : Radius

A circle has the equation below. What is the circumference of the circle?

(x – 2)² + (y + 3)² = 9

Possible Answers:

$16\pi$

$3\pi$

$9\pi$

$6\pi$

Correct answer:

$6\pi$

Explanation:

The radius is 3. Yielding a circumference of $6\pi$ .

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Example Question #3 : Circumference Of A Circle

If a circle has an area of $16\pi \; in^{2}$ , what is the circumference?

Possible Answers:

$8\pi \; in$

$4\pi \; in$

$10\pi \; in$

$12\pi \; in$

$6\pi \; in$

Correct answer:

$8\pi \; in$

Explanation:

For a circle, the formula for area is $A = \pi r^{2}$ and the formula for circumference is $C=\pi d$ , where is the radius and is the diameter.

Plug the known quantities into the area formula and solve for the radius:

$16\pi =\pi r^{2}$

$r=4\; in$

Now plug this value into the circumference formula to solve:

$C = \pi d = \pi 2r = \pi 2(4) = 8\pi\; in$

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Example Question #201 : Plane Geometry

Line is the radius of the circle shown and has a length of 7.5. What is the circumference of the circle?

Circle

Possible Answers:

$15\pi$

$30\pi$

$7.5\pi$

Correct answer:

$15\pi$

Explanation:

Plug in the given value for the radius to find the circumference:

$C=2\pi r$

$C=2(7.5)\pi=15\pi$

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Example Question #4 : Circumference Of A Circle

Find the circumference of a circle with a radius of .

Possible Answers:

$\pi$

$4\pi$

$2\pi$

$6\pi$

Correct answer:

$4\pi$

Explanation:

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

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

Solve.

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

Simplify.

$\text{Circumference}=4\pi$

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Example Question #4 : Circumference Of A Circle

Find the circumference of a circle that has a radius of $\frac{1}{2}$ .

Possible Answers:

$\pi$

$\frac{1}{2}\pi$

$-\pi$

$2\pi$

Correct answer:

$\pi$

Explanation:

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

$\text{Circumference}=2\times \frac{1}{2} \times\pi$

Solve.

$\text{Circumference}=\frac{2}{2} \times\pi$

Simplify.

$\text{Circumference}= \pi$

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Example Question #5 : Circumference Of A Circle

Find the circumference of the circle with a radius of .

Possible Answers:

$20\pi$

$10\pi$

$5\pi$

$100\pi$

Correct answer:

$20\pi$

Explanation:

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

$\text{Circumference}=2\times 10 \times\pi$

Solve.

$\text{Circumference}=20\times\pi$

Simplify.

$\text{Circumference}=20\pi$

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Example Question #6 : Circumference Of A Circle

Find the circumference of a circle with a radius of 0.9 .

Possible Answers:

$0.64\pi$

$1.8\pi$

$0.81\pi$

$0.9\pi$

Correct answer:

$1.8\pi$

Explanation:

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

$\text{Circumference}=2\times 0.9 \times\pi$

Solve.

$\text{Circumference}=1.8\times\pi$

Simplify.

$\text{Circumference}=1.8\pi$

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Example Question #202 : Basic Geometry

Find the circumference of a circle with a radius of 2.4 .

Possible Answers:

$4.8\pi$

$1.2\pi$

$9.6\pi$

$2.4\pi$

Correct answer:

$4.8\pi$

Explanation:

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

$\text{Circumference}=2\times 2.4 \times\pi$

Solve.

$\text{Circumference}=4.8\times\pi$

Simplify.

$\text{Circumference}=4.8\pi$

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Example Question #203 : Basic Geometry

Find the circumference of a circle with a radius of .

Possible Answers:

$75\pi$

$2500\pi$

$50\pi$

$100\pi$

Correct answer:

$100\pi$

Explanation:

Recall the formula for finding the circumference of a circle:

$\text{Circumference}=2\times\text{radius}\times\pi$

We can substitute in the value for the radius in order to find the circumference of the circle in question.

$\text{Circumference}=2\times 50 \times\pi$

Solve.

$\text{Circumference}=100 \times\pi$

Simplify.

$\text{Circumference}=100\pi$

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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #45 : Radius

Example Question #46 : Radius

Example Question #3 : Circumference Of A Circle

Example Question #201 : Plane Geometry

Example Question #4 : Circumference Of A Circle

Example Question #4 : Circumference Of A Circle

Example Question #5 : Circumference Of A Circle

Example Question #6 : Circumference Of A Circle

Example Question #202 : Basic Geometry

Example Question #203 : Basic Geometry

All Basic Geometry Resources

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