How to find circumference - SAT Math
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A 6 by 8 rectangle is inscribed in a circle. What is the circumference of the circle?
A 6 by 8 rectangle is inscribed in a circle. What is the circumference of the circle?
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_.
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_.
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A circle with an area of 13_π_ in2 is centered at point C. What is the circumference of this circle?
A circle with an area of 13_π_ in2 is centered at point C. What is the circumference of this circle?
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_.
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_.
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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?
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?
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 circumference is simply
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 
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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?
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?
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.
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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If a circle has an area of 
, what is the circumference of the circle?
If a circle has an area of
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.
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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A car tire has a radius of 18 inches. When the tire has made 200 revolutions, how far has the car gone in feet?
A car tire has a radius of 18 inches. When the tire has made 200 revolutions, how far has the car gone in feet?
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.
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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A circle has the equation below. What is the circumference of the circle?
(x – 2)2 + (y + 3)2 = 9
A circle has the equation below. What is the circumference of the circle?
(x – 2)2 + (y + 3)2 = 9
The radius is 3. Yielding a circumference of 
.
The radius is 3. Yielding a circumference of
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The diameter of a circle is defined by the two points (2,5) and (4,6). What is the circumference of this circle?
The diameter of a circle is defined by the two points (2,5) and (4,6). What is the circumference of this circle?
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.
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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Find the circumferencce fo a circle given radius of 7.
Find the circumferencce fo a circle given radius of 7.
To solve, simply use the formula for the circumference of a circle. Thus,
Like the prior question, it is important to think about dimensions if you don't remember the exact formula. Circumference is 1 dimensional, so it makes sense that the variable is not squared as cubed. If you rather, you can use the following formula, but realize by defining diameter, it equals the prior one.
Thus,
To solve, simply use the formula for the circumference of a circle. Thus,
Like the prior question, it is important to think about dimensions if you don't remember the exact formula. Circumference is 1 dimensional, so it makes sense that the variable is not squared as cubed. If you rather, you can use the following formula, but realize by defining diameter, it equals the prior one.
Thus,
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The area of a circle is 
. What is its circumference?
The area of a circle is
First, let's find the radius r of the circle by using the given area.
Now, plug this radius into the formula for a circle's circumference.
.
First, let's find the radius r of the circle by using the given area.
Now, plug this radius into the formula for a circle's circumference.
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The surface area of a sphere is 
.
is a point on the surface of the sphere; 
is the point on the sphere farthest from 
. A curve is drawn from 
to 
entirely on the surface of the sphere. Give the length of the shortest possible curve fitting this description.
The surface area of a sphere is
Below is a sphere with its center 
and with points 
and 
as described.
For 
and 
to be on the surface of the sphere and to be a maximum distance apart, they must be endpoints of a diameter of the sphere. The shortest curve connecting them that is entirely on the surface is a semicircle whose radius coincides with that of the sphere. Therefore, first find the radius of the sphere using the surface area formula
Setting 
and solving for 
:
The length of the curve is half the circumference of a circle with radius 10, or
Substituting 10 for 
, this is
.
Below is a sphere with its center
For
Setting
The length of the curve is half the circumference of a circle with radius 10, or
Substituting 10 for
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Give the circumference of a circle with the following diameter:
Give the circumference of a circle with the following diameter:
The circumference of a circle is its diameter multiplied by 
, so, since the diameter is 100, the circumference is simply 
.
The circumference of a circle is its diameter multiplied by
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