Question

From a solid right circular cylinder of height 2.4 cm and radius 0.7 cm, a right circular cone of same height and same radius is cut out. Find the total surface area of the remaining solid.

Answer 1

Given that,

Height (h) of the conical part = Height (h) of the cylindrical part = 2.4 cm

Radius (r) of the cylindrical part = 0.7 cm

Slant height (l) of conical part = `sqrt(r^2 + h^2)`

= `sqrt((0.7)^2 + (2.4)^2) = sqrt(0.49 + 5.76)`

`= sqrt(6.25) = 2.5`

Total surfece area of the remaining soild will be 

= CSA of cylindrical part + CSA of conical part +  Area of cylindrical base

`= 2pirh + pirl + pir^2`

`= 2 xx 22/7 xx 0.7 xx 2.4 + 22/7 xx 0.7 xx 2.5 + 22/7 xx 0.7 xx 0.7`

= 4.4 x 2.4 + 2.2 xx 2.5 + 2.2 xx 0.7

= 10.56 + 5.50 + 1.54 = 17.60 cm²

The total surface area of the remaining solid is 17.60 cm²