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Question
If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:
Options
1 : 2
2 : 1
1 : 4
4 : 1
Solution
Let the radius and height of the original cylinder be r and h respectively.
∴Volume of the original cylinder = πr2h
According to the question, radius of the new cylinder is halved keeping the height same.
⇒ Radius of the new cylinder`=r/2`
Also, height of the new cylinder = h
∴ Volume of the new cylinder `pi(r/2)^2h=(pir^2h)/4`
`\text{Volume of the new cylinder}/\text{Volume of original cylinder}=(((pir^2h)/4))/(r^2h4)=underline1=1:4`
Hence, the correct answer is C.
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