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

Let the base radius of the cylinder be rand height be h.

Radius of the reduced cylinder will be r/2 and height will be same that is h

Volume of the reduced cylinder=π(r/2)2h=π(r2/4)h

Volume of the original cylinder=πr2h

Ratio of reduced cylinder to original cylinder=

π(r2/4)h:πr2h

After simplification we get

1/4:1=1:4.

So the ratio is 1:4.

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