What happens to curved surface area of a cone if its radius and height both are doubled?

Asked by Divyaa | 25th Mar, 2017, 12:11: PM

Expert Answer:

begin mathsize 16px style Let space the space radius space of space the space cone space be space straight r space and space the space slant space height space of space the space cone space be space straight h.
So comma space the space slant space height equals straight l equals square root of straight r squared plus straight h squared end root
So comma space the space curved space surface space area space of space the space cone space equals space πrl
If space the space radius space and space the space height space are space doubled space that space is space they space become space 2 straight r space and space 2 straight h comma
then space thenew space slant space height space becomes
equals square root of left parenthesis 2 straight r right parenthesis squared plus left parenthesis 2 straight h right parenthesis squared end root
equals square root of 4 straight r squared plus 4 straight h blank squared end root
equals square root of 4 left parenthesis straight r squared plus straight h squared right parenthesis end root
equals 2 square root of straight r squared plus straight h squared end root
equals 2 straight l
That space is space the space slant space height space becomes space twice space the space old space slant space height.
So comma space the space new space curved space surface space area space equals πrl equals straight pi left parenthesis 2 straight r right parenthesis left parenthesis 2 straight l right parenthesis equals 4 left parenthesis πrl right parenthesis equals 4 space old space curved space surface space area space
Hence comma space the space new space curved space surface space area space space becomes space four space times space the space old space curved space surface space area. end style

Answered by Rebecca Fernandes | 25th Mar, 2017, 05:25: PM