Question

a cylinder has a circumgerence of 12pi cm and a height that is half the radius. what is the total surface

Answer 1

$\bf \textit{circumference of a circle}\\\\ C=2\pi r\quad \begin{cases} r=radius\\ -----\\ C=12\pi \end{cases}\implies 12\pi =2\pi r\implies \cfrac{12\pi }{2\pi }=r\implies 6=r\\\\ -------------------------------\\\\ \textit{total surface of a cylinder}\\\\ S=2\pi r(h+r)\quad \begin{cases} r=6\\ h=\stackrel{half~of~r}{3} \end{cases}\implies S= 2\pi (6)(3+6)$

and surely you know how much that is.