SOLUTION: Find, in terms of π, the surface area of a sphere generated by rotating a semicircle of radius 6 inches about its diameter.

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Question 1043641: Find, in terms of π, the surface area of a sphere generated by rotating a semicircle of radius 6 inches about its diameter.
Found 2 solutions by ikleyn, robertb:
Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
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Find, in terms of π, the surface area of a sphere generated by rotating a semicircle of radius 6 inches about its diameter.
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The solid body which is generated by rotating semicircle about its diameter is a sphere of the radius 6 inches.


The surface area of this sphere is 4%2Api%2AR%5E2 = 4%2Api%2A6%5E2 = 4%2Api%2A36 = 144%2Api.

Answer.  144%2Api.


Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Without loss of generality, let the semicircle of radius 6 be represented by the equation
y+=+sqrt%2836-x%5E2%29.
Then the surface area is obtained by rotating a rectangle with radius y+=+sqrt%2836-x%5E2%29 and width dx around the x-axis.
The element of surface area is then given by
dA+=+2%2Api%2Asqrt%2836-x%5E2%29dx.
The surface area is gotten by adding this infinite number of infinitesimal elements of surface area--