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

Original Volume:: V = pi*r^2*h

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Modified Volume::

V' = pi(r/2)^2*h

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V' = (1/4)pi*r^2*h

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Ratio of new to original:: V'/V = (1/4)pir^2h/(pir^2h) = 1/4 = 1:4

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