volumes by cross sections - swl.k12.oh.us cross sections.pdf · 1 volumes by cross sections given a...
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VOLUMES BY CROSS SECTIONS
Given a solid, bounded by two parallel planes perpendicular to x‐axis at x =a and x = b, where each cross‐sectional area is perpendicular to the x‐axis.
CROSS SECTIONS TAKEN PERPENDICULAR TO Y‐AXIS
CROSS SECTIONS TAKEN PERPENDICULAR TO X‐AXIS
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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 #1: A SQUARE
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EX #2: A SEMICIRCLE
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EX #3: An EQUILATERAL TRIANGLE
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EX #4: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 are rectangles for which the height is four times the base
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EX #5: Find the volume of the solid whose base is the region bounded by the lines and
if the cross sections taken perpendicular to the x‐axis are semicircles.
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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..