SOLUTION: A sphere with a diameter of 16 mm has the same surface area as the total surface area of a right cylinder with the base diameter equal to the sphere diameter. How high is the cylin

Question 230606: A sphere with a diameter of 16 mm has the same surface area as the total surface area of a right cylinder with the base diameter equal to the sphere diameter. How high is the cylinder?
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A sphere with a diameter of 16 mm has the same surface area as the total surface area of a right cylinder with the base diameter equal to the sphere diameter. How high is the cylinder?
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Surface of the sphere = 4*pi*r^2 = 256pi
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Surface of cylinder = 2pi*r*h + 2pi*r^2 = 256pi
pi*r*h + pi*r^2 = 128pi
pi*8*h + 64pi = 128pi
8h = 64
h = 8

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Half of the diameter.

The surface area of a sphere is given by:

The total surface area of a right cylinder is given by:

Since the diameter of the sphere is equal to the diameter of the base of the cylinder, the radii must also be equal so if the surface areas are equal, we can say:

A little algebra gets us:

Divide by

which is half the diameter.

John

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