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6\pi r^2 = 54\pi
Dividing both sides by \(6\pi\), we get:
r^2 = 9
Taking the square root of both sides, we find:
r = 3
Thus, the radius of the cylinder is \(\boxed{3}\).
Question:** A cone has a slant height of \(10\) units and a base radius of \(6\) units. Calculate the lateral surface area of the cone.
The lateral surface area \(A\) of a cone is given by:
A = \pi r l
where \(r\) is the base radius and \(l\) is the slant height. Substituting the given values \(r = 6\) and \(l = 10\), we have: