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(52811) (Show Source): You can put this solution on YOUR website! .
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 = = = .
Answer. .
Answer by robertb(5830) (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
.
Then the surface area is obtained by rotating a rectangle with radius and width dx around the x-axis.
The element of surface area is then given by
.
The surface area is gotten by adding this infinite number of infinitesimal elements of surface area--