Chapter 6 | Applications of Integration
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113. Find the volume of a sphere of radius R with a cap of height h removed from the top, as seen here.
108. The base is the region between y = x and y = x 2 . Slices perpendicular to the x -axis are semicircles. 109. The base is the region enclosed by the generic ellipse ⎛ ⎝ x 2 / a 2 ⎞ ⎠ + ⎛ ⎝ y 2 / b 2 ⎞ ⎠ =1. Slices perpendicular to the x -axis are semicircles. 110. Bore a hole of radius a down the axis of a right cone and through the base of radius b , as seen here.
111. Find the volume common to two spheres of radius r with centers that are 2 h apart, as shown here.
112. Find the volume of a spherical cap of height h and radius r where h < r , as seen here.
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