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PSAT Math : How to find circumference

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Example Questions

Example Question #1 : How To Find Circumference

If a circle has an area of $81\pi$ , what is the circumference of the circle?

Possible Answers:

$90\pi$

$81\pi$

$27\pi$

$18\pi$

$9\pi$

Correct answer:

$18\pi$

Explanation:

The formula for the area of a circle is πr². For this particular circle, the area is 81π, so 81π = πr². Divide both sides by π and we are left with r²=81. Take the square root of both sides to find r=9. The formula for the circumference of the circle is 2πr = 2π(9) = 18π. The correct answer is 18π.

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Example Question #43 : Radius

A circle with an area of 13π in² is centered at point C. What is the circumference of this circle?

Possible Answers:

13π

√13π

√26π

2√13π

26π

Correct answer:

2√13π

Explanation:

The formula for the area of a circle is A = πr².

We are given the area, and by substitution we know that 13π = πr².

We divide out the π and are left with 13 = r².

We take the square root of r to find that r = √13.

We find the circumference of the circle with the formula C = 2πr.

We then plug in our values to find C = 2√13π.

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Example Question #2 : How To Find Circumference

A 6 by 8 rectangle is inscribed in a circle. What is the circumference of the circle?

Possible Answers:

12π

8π

25π

10π

6π

Correct answer:

10π

Explanation:

First you must draw the diagram. The diagonal of the rectangle is also the diameter of the circle. The diagonal is the hypotenuse of a multiple of 2 of a 3,4,5 triangle, and therefore is 10.
Circumference = π * diameter = 10π.

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Example Question #2 : How To Find Circumference

A gardener wants to build a fence around their garden shown below. How many feet of fencing will they need, if the length of the rectangular side is 12 and the width is 8?

Screen_shot_2013-03-18_at_4.54.03_pm

Possible Answers:

40 ft.

96 ft

8π + 24

4π + 24

Correct answer:

8π + 24

Explanation:

The shape of the garden consists of a rectangle and two semi-circles. Since they are building a fence we need to find the perimeter. The perimeter of the length of the rectangle is 24. The perimeter or circumference of the circle can be found using the equation C=2π(r), where r= the radius of the circle. Since we have two semi-circles we can find the circumference of one whole circle with a radius of 4, which would be 8π.

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Example Question #3 : How To Find Circumference

The diameter of a circle is defined by the two points (2,5) and (4,6). What is the circumference of this circle?

Possible Answers:

π√5

2.5π

None of the other answers

π√2.5

5π

Correct answer:

π√5

Explanation:

We first must calculate the distance between these two points. Recall that the distance formula is:√((x₂ - x₁)² + (y₂ - y₁)²)

For us, it is therefore: √((4 - 2)² + (6 - 5)²) = √((2)² + (1)²) = √(4 + 1) = √5

If d = √5, the circumference of our circle is πd, or π√5.

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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 #1 : How To Find Circumference

6_equal_part-circle

If a circle (shown above) with area $\small 36\pi$ is divided into 6 equal slices, what is the arc length of one of the slices?

Note: The above figure is not necessarily drawn to scale.

Possible Answers:

$\small 4\pi$

$\small 2\pi$

$\small 12\pi$

$\small 6\pi$

$\small 9\pi$

Correct answer:

$\small 2\pi$

Explanation:

Begin by solving for the circumference of the circle. Use the area of the circle, which is given, and the equation for the area of a circle to determine the radius of the circle:

$\small \pi r^2$ = $\small 36\pi$

Divide both sides by $\small \pi$ .

$\small \small \frac{\pi r^2}{\pi}}$ = $\small \small \frac{36\pi}{\pi}$

$\small r^2 = 36$

Solve for :

$\small \sqrt{r^2}=\sqrt{36}$

$\small r=6$

The radius of the circle is 6. Now find the circumference.

Circumference is equal to 2 times the radius multiplied by $\small \pi$ .

$\small C=2r\pi$

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

$\small C = 12\pi$

Now that we have the circumference, divide by 6 to find the length of one of the slices of the circle:

$\small 12\pi/6 = 2\pi$

The arc length of one of the slices of the circle is $\small 2\pi$ .

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Example Question #1 : How To Find Circumference

Ashley has a square room in her apartment that measures 81 square feet. What is the circumference of the largest circular area rug that she can fit in the space?

Possible Answers:

$10\pi$

$8\pi$

$81\pi$

$18\pi$

$9\pi$

Correct answer:

$9\pi$

Explanation:

In order to solve this question, first calculate the length of each side of the room.

A=s^2

81=s^2

s=9

The length of each side of the room is also equal to the length of the diameter of the largest circular rug that can fit in the room. Since $C=\pi d$ , the circumference is simply

$C=9\pi$

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PSAT Math : How to find circumference

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : How To Find Circumference

Example Question #43 : Radius

Example Question #2 : How To Find Circumference

Example Question #2 : How To Find Circumference

Example Question #3 : How To Find Circumference

Example Question #45 : Radius

Example Question #46 : Radius

Example Question #1 : How To Find Circumference

Example Question #1 : How To Find Circumference

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