Problema Solution
the radius of a cylindrical tank is doubled while the lateral surface area remains unchanged. what is the height of the cylinder?
Answer provided by our tutors
if the original cylinder has radius r and height h then the lateral surface of the original cylinder is L = 2r(pi)h
the new cylinder has radius r1 = 2r and height h1
the lateral surface of the new cylinder is L1 = 2r1(pi)h1 = 2(2r)(pi)h1 = 4r(pi)h1
we know that the lateral surface remains unchanged that is L = L1
2r(pi)h = 4r(pi)h1
by solving the equation for h1 we find
h1 = h/2
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the height of the new cylinder is half the height of the original cylinder.