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`]

Answer 1

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`}