Is the value of $\pi$ in 2d the same in 3d? [closed]

I am starting with my question with the note "Assume no math skills". Given that, all down votes are welcomed. (At the expense of better understanding of course!)

Given my first question: What is meant by the perimeter of a Sector

1. Why is the value of $\pi$ not exactly $3$? why is it $3.14$.......... or a fraction $\frac{22}{7}$?
2. Is the value of $\pi$ of $3.14$... or $\frac{22}{7}$ the same as for $3$ dimensions?

There are several ways to define $\pi$, but whichever you choose it is a number that happens to be irrational (it's not equal to any fraction, although some fractions are close). It does represent the ratio between a circle's circumference and diameter for any circle (but not for spheres, squares, or other shapes).
I'm not exactly sure what you mean by the value of $\pi$ for 3 dimensional applications. $\pi$ is a constant value - it is always equal to $3.1415 \ldots$.
Of course formulas don't always translate the same from 2 dimensional to 3 dimensional. For example, the area of a circle is $\pi r^2$ but the volume contained within a sphere is $\frac{4\pi}{3} r^3$. You could almost say that $\pi$ in 2 dimensional geometry is analogous to $\frac{4\pi}{3}$ but then this causes fault in other places with $\pi$, such as surface area.
• it s not true that $\pi$is always a constant, the value of $pi$ depends on number of things; for example to see how $\pi$ could be equal to 42 look at this : math.stackexchange.com/questions/254620/… Commented May 18, 2013 at 22:35
• Area of a sphere is not $\frac{4}{3}\pi r^3$. This is the volume of a ball. Area of a sphere is $4\pi r^2$. Commented May 18, 2013 at 23:48