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Question
Choose the correct answer of the following 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 base radius and height of the original cylinder be r and h, respectively
Also,
The radius of the cylinder, `"R" = "r"/2` and its height, H = h.
Now,
The ratio of the volume of the new cylinder to that of the original cylinder`="Volume of the new cylinder"/"Volume of the original cylinder" `
`=(pi"r"^2"h")/(pi"R"^2"H")`
`=(pi"r"^2"h")/(pi("r"/2)^2"h")`
`= (4pi"r"^2"h")/(pi"r"^2"h")`
`=4/1`
= 4 : 1
Hence, the correct answer is option (d).
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