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

HEllo

Area of a cylinder 2πrh…..Original (formula)

Where ‘r' is the radius ‘h' is the height.

If the radius of the cylinder is halved r*1/2 & height is same ‘h', the new or reduced area of the cylinder is as follows

2π(r/2)*h = πrh

The ratio of the area of the reduced cylinder & the original one =

πrh : 2πrh

1 :2