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Question
The radius of the base of a right circular cylinder is tripled and the height is doubled. What is the ratio of volume of the new cylinder to that of the original cylinder?
Solution
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 = 3r
And, height = 2r
∴ Volume of new cylinder
= π x (3r)2 x 2h
= 18π r2h
Ratio of volume of new cylinder to that of original cylinder
= `(18π"r"^2"h")/(π"r"^2"h")`
= 18 : 1.
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