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प्रश्न
The radius of the base of a right circular cylinder is doubled and the height is halved. What is the ratio of volume of the new cylinder to that of the original cylinder?
उत्तर
Let the radius of base of the original cylinder = r
And the height of the cylinder = h
Volume of original cylinder = π r2 h
Given that, the radius of new cylinder = 2r
And height= `"h"/(2)`
∴ Volume of new cylinder
= `π xx (2"r")^2 xx "h"/(2)`
= 2 x r2h
Ratio of volume of new cylinder to that of original cylinder
= `(2pi"r"^2"h")/(pi"r"^2"h")`
= 2 : 1.
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