Why 2 pi r

Ask if either of these are what you were looking for. If we imagine the circle centered in the origin with radius r , it has the equation:.

And considering the fourth of circle in the first quadrant, we can obtain the lenght of a line with the integral:. I don't think you can prove it, because that is, or is equivalent, to the definition of pi. However, in both cases there are alternative definition in terms of limits of infinite series , but if you go down that path you just go round in circles: you can arbitrarily pick any one of the relationships as a definition and show that the others necessarily follow, and that they are all related to the same quantity, be it pi or e.

Evaluating pi or e is a different matter entirely. Viewed 23k times. Matt Gregory Matt Gregory 1, 3 3 gold badges 17 17 silver badges 26 26 bronze badges. I just thought I'd clarify your comment, since, unfortunately, the "window" in which to edit comments expires! Add a comment. Active Oldest Votes. Guillaume Martres Guillaume Martres 4 4 silver badges 9 9 bronze badges. Thank you! Henry Henry k 9 9 gold badges silver badges bronze badges. Sign up or log in Sign up using Google.

Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Remember to add you units to the final answer. Practice with an example.

Understand surface area. What is the formula for volume? Calculating Volume The formula to find the volume multiplies the length by the width by the height. The good news for a cube is that the measure of each of these dimensions is exactly the same.

Therefore, you can multiply the length of any side three times. How do you find a surface area of a cylinder? To find the surface area of a cylinder add the surface area of each end plus the surface area of the side.

What is the meaning of lateral surface area? The lateral surface of an object is the area of all the sides of the object, excluding the area of its base and top. For a cube, the lateral surface area would be the area of four sides. Is surface area squared or cubed? Look Out: surface area is only two-dimensional and is expressed as units squared, not units cubed.