Young's modulus in code

You will write four functions for Searle's experiment. They follow the lesson.

The idea. For a wire of diameter $d$ and length $L$, $Y = \dfrac{4MgL}{\pi d^2\,\Delta L}$. A line through the origin fitted to the extension against the load has the slope $\dfrac{\sum M\,\Delta L}{\sum M^2}$, and then $Y = \dfrac{4gL}{\pi d^2 \times \text{slope}}$.

Your tasks.

1. In area, return the area of cross-section of a wire of diameter d, in the same units as d squared.
2. In youngs_one, return $Y$ from one pair of readings: load m in kg, extension dl in m, length L in m and diameter d in m.
3. In slope_origin, return the slope of the line through the origin: the sum of load times extension divided by the sum of load squared.
4. In youngs_slope, return $Y$ from the slope in m/kg, the length and the diameter.