Question

Find the ratio of volume of cylinder. When the radius is halved, and the height is same to that of volume of cylinder.​

Answer 1

$\sf \underline {\underline{ANSWER}} \\ \\ \sf Given, \\ \: \: \: \: \: \: \: \: \: \: \: \sf original \: volume \: (v_{1}) = \pi{r}^{2} h \\ \sf \: \: \: \: \: \: \: \: \: \: \: reduced \: length \: (v _{2}) \: = \\ \\ \tt{ \star } \: \: radius \: is \: halved \\ \tt \star \: \: height \: is \: same \\ \\ \sf = \pi(\frac{r}{2} )^{2} h \\ \\ \\ \therefore \sf ratio \: = \frac{\pi \times r \times r \times h }{ \pi \times \frac{r}{2} \times \frac{r}{2} \times h} = \bf \red {1 : 4}$

Answer 2

volume of cylinder =πr^h........(1)

new volume when volume is halved

now r=r/2

volume'=π(r/2)^2 xh...........(2)

dividing 1 from 2

v/v'=πr^2 h/π(r/2)^2 xh

now π and h will be canceled out

v/v'=r^2/(r/2)^2

rxr/r/2 xr/2


1/4

1:4 is ur answer