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The radius of the base of a right cylinder is halved, keeping the height same. What is the ratio of the volume of the cylinder thus obtained to the volume of the original cylinder?

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1:4

2:9

6:8

7:9

answer is A.

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Detailed Solution

Let radius and height be r and h

\Rightarrow

Volume of cylinder =

π r^{2} h

\Rightarrow

radius of new cylinder =

\frac{r}{2}

……..(given)

\Rightarrow

Volume of new cylinder =

π {(\frac{r}{2})}^{2} h

\frac{π r^{2} h}{4}

\Rightarrow \frac{Volume of new cylinder}{Volume of original cylinder}

\frac{\frac{π r^{2} h}{4}}{π r^{2} h}

\frac{1}{4}

Hence, the ratio is 1:4

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