From a solid cylinder, whose height is 8 cm and radius 6 cm, a conical cavity of height 8 cm and of base radius 6 cm is hollowed out. Find the total surface area of the remaining solid.

Asked by Topperlearning User | 25th Oct, 2017, 01:58: PM

Expert Answer:

 

 

 

 

begin mathsize 12px style For space the space conical space cavity comma space radius space straight r space equals space 6 space cm comma space height space equals space 8 space cm
rightwards double arrow space slant space height space equals space straight l space equals space square root of straight h squared space plus space straight r squared end root space equals space square root of 8 squared space plus space 6 squared end root space equals space 10 space cm
For space cylinder space straight r space equals space 6 space cm comma space height space equals space 8 space space cm
the space total space surface space area space of space the space remaining space solid space
equals space Curved space surface space of space cylinder space plus space Curved space surface space of space the space cone space plus space base space of space the space cylinder
equals space 2 πrhh space plus space πrl space plus space πr squared
equals space 22 over 7 open parentheses 2 cross times 6 cross times 8 space plus space 6 cross times 10 space plus space 6 squared close parentheses
equals space 678.85 space cm squared
space space space space space space space space space space space space space space

The space surface space area space of space remaining space solid space is space space 678.85 space cm squared end style

 

Answered by  | 25th Oct, 2017, 03:58: PM