Question

The radius of a cylinder is doubled and its curved surface area is kept as same, the height of the cylinder is ______.

Options

• same

• doubled

• halved

• none of these

Answer 1

The radius of a cylinder is doubled and its curved surface area is kept as same, the height of the cylinder is halved.

Explanation:

The curved surface area of a cylinder is given by 2πrh. If the radius (r) is doubled to 2r while keeping the surface area constant, the new height (h') must satisfy 2π(2r)h' = 2πrh, which simplifies to \[4\pi r h' = 2\pi r h \implies h' = \frac{1}{2}h\], meaning the height is halved.