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Question
If the radius of the base of a right circular cylinder is halved keeping the same height, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is
Options
1 : 2
1 : 4
1 : 6
1 : 8
Solution
1 : 4
Explanation;
Hint:
Let the radius of the cylinder be "r" and the height be "h"
Radius of the new cylinder = `"r"/2` ...(Height will be same)
Volume of the new cylinder : Volume of the original cylinder
= `pi"r"_1^2"h" : pi"r"_2^2"h"` ...(πh is same)
= `pi_1^2 : "r"_2^2`
= `("r"/2)^2 : "r"^2`
= `("r"^2)/4 : "r"^2 = 1/4 : 1`
= 1 : 4
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