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Question:

From a solid cylinder of height 7cm and base diameter 12cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid. [Use π=22/7]

Solution:

Given:Height(h)of cylindrical part=height(h)of the conical part=7cmDiameter of the cylindrical part=12cmTherefore, Radius(r)of the cylindrical part=12/2=6cmSo, Radius of the conical part=6cmSlant height(l)of conical part =√r²+h²cm=√6²+7²=√36+49=√85≈9.22cm.The total surface area of the remaining solid=CSA of the cylindrical part+CSA of the conical part+Base area of the circular part=2πrh+πrl+πr²=2×22/7×6×7+22/7×6×9.22+22/7×6×6=264+173.86+113.14=551cm²