From a solid cylinder of height 36 cm and radius 14 cm, a conical cavity of radius 7 cm and height 24 cm is drilled out. Find the volume and the total surface area of the remaining solid.

Explanation

According to the given statement , the figure will be as shown alongside:
Clearly for solid cylinder height (H) =36 cm and radius (R ) =14cm.And for conical cavity height (h)=24 cm radius (c ) =7cm and slant height (l)=`(sqrt(h^(2)+r^(2))=(sqrt(24^(2)+7^(2))cm` =25cm volume of the remaining solid =volume of cylinder -volume of conical cavity
`piR^(2)H-(1)/(3)pir^(2)h`
`=(22)/(7)xx(14)^(2)xx36cm^(3)-(1)/(3)xx(22)/(7)xx(7)^(2)xx24cm^(3)`
`22176 cm^(3) - 1232 cm^(3)`
`=20944 cm^(3)`

Total surface area of the remaining solid
=Area of the base of the cylinder +cuved surface area of the cylinder +Area of the top ring + curved surface area of the conical cavity
`=piR^(2)+2piRH+pi(R^(2)-r^(2))+pirl`
`=(22)/(7)[(14^(2)+2xx14xx36+(14^(2)-7^(2))+7xx25)]cm^(2)`
`=(22)/(7)xx1526 cm^(2)=4796 cm^(2)`