Question
If the radius of a right circular cylinder is doubled
(an increase of 100%), and its height is reduced by half (a decrease of 50%), what will be the ratio of the volume of the original cylinder to the volume of the modified cylinder?Solution
Let the radius and height of the old cylinder be 'r' units and 'h' units, respectively Volume of the old cylinder = π X r2 X h = πr2h cubic units Radius of the new cylinder = r X 2 = '2r' units Height of the new cylinder = h X 0.5 = '0.5h' units So, volume of the new cylinder = π X (2r)2 X 0.5h = 2πr2h cubic units So, required ratio = πr2h:2πr2h = 1:2
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