How to find circumference
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PSAT Math › How to find circumference
A circle with an area of 13_π_ in2 is centered at point C. What is the circumference of this circle?
2√13_π_
√13_π_
26_π_
√26_π_
13_π_
Explanation
The formula for the area of a circle is A = _πr_2.
We are given the area, and by substitution we know that 13_π_ = _πr_2.
We divide out the π and are left with 13 = _r_2.
We take the square root of r to find that r = √13.
We find the circumference of the circle with the formula C = 2_πr_.
We then plug in our values to find C = 2√13_π_.
If a circle has an area of 
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.
A circle has the equation below. What is the circumference of the circle?
(x – 2)2 + (y + 3)2 = 9
Explanation
The radius is 3. Yielding a circumference of 
A 6 by 8 rectangle is inscribed in a circle. What is the circumference of the circle?
6_π_
8_π_
10_π_
25_π_
12_π_
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 = 10_π_.
A car tire has a radius of 18 inches. When the tire has made 200 revolutions, how far has the car gone in feet?
600π
3600π
300π
500π
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.
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?
96 ft
40 ft.
8π + 24
4π + 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.
If a circle (shown above) with area 
Note: The above figure is not necessarily drawn to scale.
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:
Divide both sides by 
Solve for 
The radius of the circle is 6. Now find the circumference.
Circumference is equal to 2 times the radius multiplied by 
Now that we have the circumference, divide by 6 to find the length of one of the slices of the circle:
The arc length of one of the slices of the circle is 
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?
Explanation
In order to solve this question, first calculate the length of each side of the room.
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 
The diameter of a circle is defined by the two points (2,5) and (4,6). What is the circumference of this circle?
None of the other answers
2.5π
5π
π√2.5
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.