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

\( Area\ of\ base: A_B=169\pi\ ft^2\\\\A_B=\pi r^2\ \ \ (r-radius)\\\\\pi r^2=169\pi\ \ \ /:\pi\\\\r^2=169\\\\r=\sqrt{169}\\\\r=13\ (ft)\\\\H=2r\to H=2\cdot13=26\ (ft) \)

\( lateral\ area: A_L=2\pi rH\\\\A_L=2\pi\cdot13\cdot26=676\pi\ (ft^2)\\\\Surface\ area: A_S=2A_B+A_L\\\\A_S=2\cdot169\pi+676\pi=338\pi+676\pi=1014\pi\ (ft^2) \)

Area of base = 169 π 

r = √Area = 13 ft


Given, height = 2 x 13 = 26 ft.

Lateral surface area of cylinder = 2πrh = 2 x π x 13 x 26 = 676 π ft²

Total surface area = 2πr(r + h) = 2 x π x 13 x 39 = 1014 π ft²

Thus, lateral surface area is 676 ft² and total surface area is 1014 ft²


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