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

$\huge{\mathfrak{\underline{Solution:}}}$

$\textsf{Let the radius of the Original Cylinder = r} \\ </p><p></p><p>\textsf</p><p></p><p>{And its height = h} \\ \\ </p><p></p><p>\sf Now, \\ \textsf{The Radius of Reduced Cylinder} \sf= \dfrac{r}{2} \\ \textsf</p><p></p><p>{Height = h} \\ \\ \therefore \sf \frac{Volume \: of \: Reduced \: Cylinder}{Volume \: of \: Original \: Cylinder} \\ \Rightarrow \sf \frac{\pi { \bigg(\dfrac{r}{2} \bigg)}^{2} \times h }{\pi \times r \times h} \\ \Rightarrow \sf \frac{1}{4} \\ \\ \textsf {Hence the ratio is 1 : 4.}$