Question

From a solid cylinder of height 7 cm and base diameter 12cm,a conical cavity of same height and smae base diameter is hollowed out. Find the total surface area of the remaining solid upto two decimal places. [Take root 85 =9.2]

Answer 1

v of cylinder = πr²h
∴v of cone = 1/3 πr²h
∴we can take h=7cm , d=12cm, r=6cm
surface area of a cone=πrl when l=slant height of cone.
to find the slant height:
draw a perpendicular from top vertex to the mid of the diameter.
∴slant height = √(7²+6²) = √85 = 9.2
∴surface area of the cone = π * 6 *9.2
                                           = 173.48 cm²