Question

in a cylinder its radius is halved and height is doubled then find the ratio of volume of original to new one.

Answer 1

Original Volume of cylinder= 22/7 x r^2 x h

when radius= r/2 and height= 2h

then new volume= 22/7 x (r/2)^2 x (2h)

Original volume/ new volume= 2

therefore when radius is halved and height is doubled then the new volume becomes 1/2 times of the original volume.

Answer 2

Volume of a cylinder = $\pi$ r²h
original volume         = $\pi$ r²h
new radius               =r/2
new height               =2h
mew volume            = $\pi$ (r/2)² × 2h
                              = $\pi$ r²/4 × 2h
                              = $\pi$ r²/2 × h
Volume of original cylinder : volume of new cylider =$\pi$ r²h: $\pi$ r²/2 × h
                                                                          =r² : r²/2 ($\pi$ and h                                                                                                       cancelled)
                                                                  Multiplying by 2
                                                                          = 2r² : r² (r² cancelled)
                                                                          = 2