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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)
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surface area of a sphere = 4 * pi * r^2
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set the formulas = to each other
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4 * pi * r^2 = pi * r^2 + pi * r * l
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3 * pi * r^2 = pi * r * l
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3 * r = l
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3 * r = square root(h^2 +r^2)
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square both sides of the =
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9 * r^2 = h^2 +r^2
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r^2 = h^2/8
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r = h/(2 * square root(2))
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h/r = 2 * square root(2)
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