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Exercises for calculating the volumes of solids with different base shapes and cross-sectional areas. The base shapes include squares, semicircles, and an equilateral triangle. The cross-sectional areas are determined by planes perpendicular to the x-axis. Each exercise includes a region defined by the graphs of two functions and instructions for finding the volume of the solid with that region as its base, given the shape of the cross-sections.
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Let (^) R be the region bounded by the graphs of and. Find the volume of the solid that has R as its base if every cross section by a plane perpendicular to the x ‐ axis has the given shape.
EX #3: An EQUILATERAL TRIANGLE
EX #6: Find the volume of the solid whose base is the region inside the circle if the cross sections taken perpendicular to the y ‐axis are squares..
