2. (6 points) A spherical cap is a heel cut off a sphere by a plane,...

 

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2. (6 points) A spherical cap is a "heel" cut off a sphere by a plane, that is a region enclosed above by a sphere and below by a plane. Use spherical coordinates to show that the volume of a spherical cap cut from a sphere with radius R and a height h from the base of the cap to its top is equal to ah (3 R-h). HINT: At some point you might want to use that the volume of a cone is equal to 1/3 base area* height. 2. (6 points) A spherical cap is a "heel" cut off a sphere by a plane, that is a region enclosed above by a sphere and below by a plane. Use spherical coordinates to show that the volume of a spherical cap cut from a sphere with radius R and a height h from the base of the cap to its top is equal to ah (3 R-h). HINT: At some point you might want to use that the volume of a cone is equal to 1/3 base area* height.

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