SOLUTION: A sphere is inscribed in a cylinder. Use complete sentences and geometric formulas to compare the surface area of the sphere and the lateral area of the cylinder.

Algebra ->  Surface-area -> SOLUTION: A sphere is inscribed in a cylinder. Use complete sentences and geometric formulas to compare the surface area of the sphere and the lateral area of the cylinder.       Log On


   

Question 1084213: A sphere is inscribed in a cylinder. Use complete sentences and geometric formulas to compare the surface area of the sphere and the lateral area of the cylinder.
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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1.  Let "r" be the radius of the sphere.

    Since the sphere is inscribed in the cylinder, the radius of the cylinder is "r" too, and the height of the cylinder is h = 2r.


2.  Surface area of the sphere is S%5Bsphere%5D = 4%2Api%2Ar.


3.  Lateral surface area of the cylinder is S%5Bcylinder%5D = 2%2Apir%2Ah = 2%2Api%2Ar%2A%282%2Ar%29 = 4%2Api%2Ar%5E2.


4.  Comparing these expressions, we can conclude that in the considered case 


            the surface area of the sphere is equal to the lateral area of the cylinder.

Solved.