182. Find the diameter of a circle with an area of 100.
182. Al-Karhi's Solution: Let the diameter be $x$, the square of it $x^{2}$. Subtract $\frac{1}{7}+\frac{1}{7} \cdot \frac{1}{2}$ of the square of the diameter. The remainder

$$
\frac{5}{7} x^{2}+\frac{1}{7} \cdot \frac{1}{2} x^{2}=100 ; x^{2}=127 \frac{3}{11}=\frac{1400}{11}
$$

Common solution: $\frac{\pi d^{2}}{4}=100 ; d^{2}=\frac{400}{\pi} ;$ therefore, $\frac{400}{\pi}=\frac{1400}{11}$ or $\pi=\frac{22}{7}$. Thus, if $\frac{11}{14}$ of the square of the diameter 118
is considered the area of the circle, then the result is the Archimedean approximation for $\pi$.