Volume Of Cube Cuboid And Cylinder

Let the radius of the base be , and the height of the cylinder be . The area of the cross-section (which is the area of the circular base) is given by: The volume of the cylinder is given by: We are told that the area of the cross-section is doubled, meaning the new area . Since the area of the base is proportional to the square of the radius, if the area is doubled, the radius will increase by a factor of . Now, let's find the ratio of the new height to the new radius . Since the volume of the cylinder remains constant, the volume equation becomes: Using the relationship , we substitute the values: Substituting , we get: Simplifying: Thus, the ratio of height and radius is .