12. \(\dfrac{4\sqrt{3}}{3}\pi\)

13. \(12\pi\)

14. \(\sqrt{6}\pi a^2\)

b: \(=\dfrac{39}{7}\cdot\dfrac{2}{9}+\dfrac{18}{7}\cdot\dfrac{-2}{9}=\dfrac{2}{9}\cdot3=\dfrac{2}{3}\)

a)\(đkx\ge1,x\ne-1\)

\(\sqrt{\dfrac{x-1}{x+1}}=2\)

\(\Leftrightarrow\dfrac{x-1}{x+1}=4\)

\(\Leftrightarrow x-1=4x-4\)

\(\Leftrightarrow x=1\)(nhận)

Vậy S=\(\left\{1\right\}\)

c)đk\(25x^2-10x+1=\) \(\left(5x-1\right)^2\ge0\Leftrightarrow x\ge\dfrac{1}{5}\)

\(\sqrt{25x^2-10x+1}+2x=1\)

\(\Leftrightarrow\sqrt{\left(5x-1\right)^2}+2x=1\)

\(\Leftrightarrow5x-1+2x=1\)

\(\Leftrightarrow x=\dfrac{2}{7}\)(nhận)

Vậy S=\(\left\{\dfrac{2}{7}\right\}\)

c: Ta có: \(\sqrt{25x^2-10x+1}+2x=1\)

\(\Leftrightarrow\left|5x-1\right|=1-2x\)

\(\Leftrightarrow\left[{}\begin{matrix}5x-1=1-2x\left(x\ge\dfrac{1}{5}\right)\\5x-1=2x-1\left(x< \dfrac{1}{5}\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{7}\left(nhận\right)\\x=0\left(nhận\right)\end{matrix}\right.\)

e: Xét tứ giác AHCN có

AH//CN

AN//CH

=>AHCN là hình bình hành

=>AH=CN=15cm

Xét tứ giác GHKI có 

GH//KI

GH=KI

Do đó: GHKI là hình bình hành

Suy ra: GI=HK