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Pre-Algebra : Perimeter

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #11 : Perimeter

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

Possible Answers:

$4\pi ^2$

$8\pi$

$2\pi ^2$

$8\pi ^2$

$4\pi$

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 #12 : Perimeter

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

Possible Answers:

$2\pi\sqrt5$

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

$2\sqrt5$

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

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

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 #12 : Circumference Of A Circle

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

Possible Answers:

$15.7\ inches$

$47.1\ inches$

$78.5\ inches$

$62.8\ inches$

$31.4\ inches$

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 #13 : Perimeter

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

Possible Answers:

$36\pi$

$6\pi$

$12\pi$

$3\pi$

$9\pi$

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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Example Question #12 : Perimeter

Alfredo ran laps around his track. He had just learned in math about circumference and was wondering what the circumference of his circular track was. He knows that the diameter of his track is 100 feet. What is the circumference of Alfredo's track?

Possible Answers:

$25\pi$

$100\pi$

$50\pi$

None of the above

$200\pi$

Correct answer:

$100\pi$

Explanation:

The only thing that needs to be known for this question is the equation for circumference which is:

$\pi$

Therefore your answer to this problem is simply

$100\pi$

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Example Question #13 : Perimeter

Susy's yard is 32 yards by 17 yards. What is the total perimeter of her yard?

Possible Answers:

$\small 98\ \textup{yards}$

$\small 544\ \textup{yards}$

$\small 108\ \textup{yards}$

$\small 49\ \textup{yards}$

Correct answer:

$\small 98\ \textup{yards}$

Explanation:

Recall, the perimeter of a rectangle = 2*length + 2*width

Using the values given to us in the problem:

$\small Perimeter = (2*34)+(2*17) = 64+34 = 98$

Thus, the perimeter is 98 yards.

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Example Question #2 : Perimeter Of A Rectangle Or Square

Sally has a rectangular garden that is surrounded by a 6ft-wide and 8ft-long fence. However, she wants to expand her garden so that it is twice as wide and twice as long. What is the new perimeter of her garden?

Possible Answers:

$48\ \textup{ft.}$

$46\ \textup{ft.}$

$56\ \textup{ft.}$

$28\ \textup{ft.}$

$50\ \textup{ft.}$

Correct answer:

$56\ \textup{ft.}$

Explanation:

We know the original garden is a 6ft by 8ft rectangle. sally wants to expand her garden so that the new rectangle is twice as long and twice as wide, so the new dimensions are 12ft by 16ft.

The perimeter of a rectangle with these dimensions is

12*2 +16*2 = 56.

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Example Question #3 : Perimeter Of A Rectangle Or Square

Choose the correct equation to solve for the perimeter of the rectangle.

Peter's backyard is a rectangle. Two sides of his lawn are feet long, and two sides of his lawn are feet long.

Possible Answers:

20 + 2(15) = 50

2(20) + 15 = 55

4(20) + 15 = 95

20 + 15 = 35

2(20) + 2(15) = 70

Correct answer:

2(20) + 2(15) = 70

Explanation:

The correct answer is 2(20) + 2(15) = 70

Rectangles have sets of equal sides. In this example, one set of these sides is feet long and one set is feet long.

Therefore, multiplying the length of each side by two then adding these together will produce the perimeter.

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Pre-Algebra : Perimeter

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #11 : Perimeter

Example Question #12 : Perimeter

Example Question #12 : Circumference Of A Circle

Example Question #13 : Perimeter

Example Question #15 : Circumference Of A Circle

Example Question #16 : Circumference Of A Circle

Example Question #12 : Perimeter

Example Question #13 : Perimeter

Example Question #2 : Perimeter Of A Rectangle Or Square

Example Question #3 : Perimeter Of A Rectangle Or Square

All Pre-Algebra Resources

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