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Question
In a cylinder, if radius is halved and height is doubled, the volume will be ______.
Options
same
doubled
halved
four times
Solution
Let V1 be the volume of the cylinder with radius r1 and height h1, then
`V_1 = pir_1^2h_1` ……. (1)
Now, let V2 be the volume after changing the dimension, then
`r_2 = 1/2r_1 , h_2 = 2h_1`
So,
`V_2 = pir_2^2 h_2 = pi xx ((r_1)/2)^2 xx 2h_1`
`⇒ V_2 = 1/2 xx pi r_1^2 h_1 = 1/2V_1`
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