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Pre-Algebra : Geometry

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11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #3 : Perimeter

Given the area of the circle is $9\pi$ , what is the circumference of the circle?

Possible Answers:

$6\pi +6$

$3+3\pi$

$6\pi$

Correct answer:

$6\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the area.

$9\pi=\pi r^2$

r^2=9

r=3

Write the circumference of the circle.

$C=2\pi r$

Substitute the radius.

$C=2\pi (3) = 6\pi$

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Example Question #4 : Perimeter

Find the circumference of a circle with an area of $\pi^2$ .

Possible Answers:

$3\pi^2$

$2\pi ^3$

$\pi \sqrt{\pi}$

$3\pi$

$2\pi \sqrt{\pi}$

Correct answer:

$2\pi \sqrt{\pi}$

Explanation:

Write the area formula in order to find the radius.

$A=\pi r^2$

Substitute the area.

$\pi ^2=\pi r^2$

$r^2=\pi$

$r=\sqrt{\pi}$

Write the circumference formula.

$C=2\pi r$

Substitute the radius.

$C=2\pi \sqrt{\pi}$

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Example Question #5 : Perimeter

Determine the circumference of the circle if the radius is $2\pi$ .

Possible Answers:

$4\pi ^2$

$4\pi$

$2\pi ^2$

$8\pi$

$4\pi ^3$

Correct answer:

$4\pi ^2$

Explanation:

Write the formula for the circumference of a circle.

$C=2\pi r$

Substitute the radius into the formula.

$C=2\pi (2\pi) = 4\pi ^2$

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Example Question #6 : Perimeter

Find the circumference of a circle with a radius of $\sqrt2$ .

Possible Answers:

$\frac{\sqrt{2\pi}}{2}$

$4\pi$

$2\pi$

$2\pi \sqrt{2}$

$\frac{\sqrt2}{2} \pi$

Correct answer:

$2\pi \sqrt{2}$

Explanation:

Write the formula to find the circumference of a circle.

$C=2\pi r$

Substitute the radius.

$C=2\pi \sqrt{2}$

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Example Question #271 : Geometry

Find the circumference of the circle with a diameter of $2\pi$ .

Possible Answers:

$8\pi$

$2\pi ^2$

$4\pi ^2$

$4\pi$

$8\pi ^2$

Correct answer:

$2\pi ^2$

Explanation:

Write the formula for the circumference of a circle.

$C=\pi D = 2\pi r$

Substitute the diameter.

$C=\pi (2\pi) = 2\pi ^2$

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Example Question #272 : Geometry

Find the circumference of a circle with an area of 5.

Possible Answers:

$2\pi\sqrt5$

$2\pi \sqrt{\frac{5}{\pi}}$

$\sqrt{\frac{2\pi}{5}}$

$2\sqrt5$

$2\pi \sqrt{\frac{5}{2\pi}}$

Correct answer:

$2\pi \sqrt{\frac{5}{\pi}}$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the area to find the radius.

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

$5=\pi r^2$

$\frac{5}{\pi }=r^2$

$r=\sqrt{\frac{5}{\pi}}$

Write the formula to find the circumference of the circle.

$C=2\pi r$

Substitute the radius.

$C=2\pi \sqrt{\frac{5}{\pi}}$

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Example Question #13 : Circumference Of A Circle

If $\pi = 3.14$ find the circumference of a circle with a diameter of 10 inches.

Possible Answers:

$62.8\ inches$

$47.1\ inches$

$15.7\ inches$

$78.5\ inches$

$31.4\ inches$

Correct answer:

$31.4\ inches$

Explanation:

To solve, we will use the formula for circumference of a circle. The formula is

$C = 2 \pi r$

where $r = \text{ radius}$ . We know that the diameter of the circle is 10 inches. To find the radius, we simply divide by 2.

Therefore,

r =5

We know $\pi = 3.14$ , so we will substitute. We get

$C = 2 \cdot 3.14 \cdot 5 \text{ inches}$

$C = 31.4 \text{ inches}$

Therefore, the circumference of the circle is 31.4 inches.

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Example Question #14 : Circumference Of A Circle

Find the circumference of a circle with a radius of 6cm.

Possible Answers:

$6\pi$

$3\pi$

$12\pi$

$36\pi$

$9\pi$

Correct answer:

$12\pi$

Explanation:

The formula to find the circumference of a circle is

$C = \pi d$

where d is the diameter. We know the radius is 6cm. We also know to find the diameter, we take two times the radius. Therefore, the diameter is 12cm. So, substituting into the formula, we get

$C = \pi \cdot 12$

$C = 12\pi$

Therefore, the circumference of the cirlce is $12\pi$ .

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Example Question #15 : Circumference Of A Circle

A circle has a radius of . What is its circumference?

Possible Answers:

$38\pi$

Not enough information given

$21\pi$

$361\pi$

$19\pi$

Correct answer:

$38\pi$

Explanation:

The formula for the circumference of a circle is

$C=2\pi r$ .

So, we simply plug in the radius of in order to solve for the circle's circumference:

$C=2\pi (19)$

$C=38\pi$

Therefore, the circumference of ths circle is $38\pi$ .

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Example Question #16 : Circumference Of A Circle

What is the distance around a silo, if the distance from the center of the silo to the outside is ?

Possible Answers:

$8\pi m$

$16\pi m$

$64\pi m$

16 m

Correct answer:

$16\pi m$

Explanation:

What is the distance around a silo, if the distance from the center of the silo to the outside is ?

Picture a silo, its base is a circle.

This problem want the circumference of that circle. It gives us the distance from the center to the outside of the circle, aka the radius.

Find circumference via the following formula:

$Circumference=2 \pi r$

$C=2*8 \pi =16\pi m$

So the distance is:

$16\pi m$

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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #3 : Perimeter

Example Question #4 : Perimeter

Example Question #5 : Perimeter

Example Question #6 : Perimeter

Example Question #271 : Geometry

Example Question #272 : Geometry

Example Question #13 : Circumference Of A Circle

Example Question #14 : Circumference Of A Circle

Example Question #15 : Circumference Of A Circle

Example Question #16 : Circumference Of A Circle

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