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# a cylinder with base are 169π ft^2 and a height twice the radius. what is the lateral area and surface area of the cylinder

$Area\ of\ base:A_B=169\pi\ ft^2\\\\A_B=\pi r^2\ \ \ (r-radius)\\\\\pi r^2=169\pi\ \ \ /:\pi\\\\r^2=169\\\\r=\sqrt{169}\\\\r=13\ (ft)\\\\H=2r\to H=2\cdot13=26\ (ft)$ $lateral\ area:A_L=2\pi rH\\\\A_L=2\pi\cdot13\cdot26=676\pi\ (ft^2)\\\\Surface\ area:A_S=2A_B+A_L\\\\A_S=2\cdot169\pi+676\pi=338\pi+676\pi=1014\pi\ (ft^2)$