SAT Math Help » Geometry » Plane Geometry » Circles » Radius » How to find circumference

If a circle has an area of

*
, what is the circumference of the circle?


*


*


*


*


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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Explanation:

The formula for the area of a circle is 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 = 2πr.

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


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.


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?

 
  

 

 

 

 


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.

 

 

 

 


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


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.


A car tire has a radius of 18 inches. When the tire has made 200 revolutions, how far has the car gone in feet?


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.


Explanation:

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,

*


Explanation:

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.

*


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.


Explanation:

Below is a sphere with its center 

*
 and with points 
*
 and 
*
 as described.

See more: Clue: City Where Galileo Taught Crossword Clue, Clue: City Where Galileo Taught

*

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 

*
.


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