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SOLVED:A spherical cap is the region of a sphere that lies above or below a given plane. a. Show that the volume of the spherical cap in the figure below is (1)/(6) πh(3 a^2 h^2).
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SOLVED:The surface area of a spherical cap is given by S=2 πr h, where r is the radius of the sphere and h is the perpendicular distance from the sphere's surface to the plane intersecting the sphere, forming the cap. The volume of the cap is V=(1)/(3) πh^2(3 r-h). Similar to Exercise 61 , a formula can be found that will minimize the area of a cap that holds a specified volume. a. Solve the volume formula for the variable r. b. Substitute the resulting expression for r into the surface area for
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