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Question
From a solid cylinder of height 7 cm and base diameter 12 cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid. [User `pi22/7`]
Solution
It is given that, height (h) of cylindrical part = height (h) of the conical part = 7 cm
Diameter of the cylindrical part = 12 cm
∴Radius (r) of the cylindrical part `12/2 cm=6cm`
∴ Radius of conical part = 6 cm
Slant height (l) of conical part `=sqrt(r^2+h^2)cm`
`=sqrt(6^2+7^2)cm`
`=sqrt(36+49)cm`
`=sqrt85cm`
`9.22 cm`
Total surface area of the remaining solid
= CSA of cylindrical part + CSA of conical part + Base area of the circular part
= 2πrh + πrl +πr2
`=2xx22/7xx6xx7cm^2+22/7xx6xx9cm^2+22/7xx6xx6cm^2`
`=264cm^2+173.86^2+113.14cm^2`
`=551cm^2`
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