SOLUTION: A cone has the same radius and surface area as a sphere. Find the ratio of the perpendicular height of the cone to the radius

Question 1127169: A cone has the same radius and surface area as a sphere. Find the ratio of the perpendicular height of the cone to the radius
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
surface area of a cone = pi * r^2 + pi * r * l, where r is radius of the circular base, l is the slant height(l = square root(h^2 +r^2), where h is the perpendicular height of the cone)
:
surface area of a sphere = 4 * pi * r^2
:
set the formulas = to each other
:
4 * pi * r^2 = pi * r^2 + pi * r * l
:
3 * pi * r^2 = pi * r * l
:
3 * r = l
:
3 * r = square root(h^2 +r^2)
:
square both sides of the =
:
9 * r^2 = h^2 +r^2
:
r^2 = h^2/8
:
r = h/(2 * square root(2))
:
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h/r = 2 * square root(2)
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