If the lateral surface area of a right circular cylinder is equal to twice the area of its base, find the height in terms of the radius.
h = r
We compare two surfaces of a right circular cylinder: its curved (lateral) surface and one flat circular base.
The lateral surface area is \(2\pi r h\), obtained by unrolling the curved surface into a rectangle of width \(2\pi r\) (the circumference) and height \(h\).
The area of the circular base is \(\pi r^2\).
The condition given is that the lateral area equals twice the base area: \(2\pi r h = 2\times \pi r^2\).
Both sides share the common factor \(2\pi r\), which is non-zero, so we may cancel it.
Cancelling gives \(h = r\).
Thus the height must equal the radius for the two areas to satisfy the stated relation.
The required relation is h = r.
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