Volumes Worksheet 6.3 - Calculus Maximus Page 8
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11Calculus Maximus
WS 6.3: Volumes
2
11. (AP 2009-4) Let R be the region in the first quadrant enclosed by the graphs of
y
2
x
and
y
x
, as
shown in the figure.
(a) Find the area of R.
(b) The region R is the base of the solid. For this solid, at each x, the cross section perpendicular to the
x-axis has area
. Find the volume of the solid.
A x
sin
x
2
(c) Another solid has the same base R. For this solid, the cross sections perpendicular to the y-axis are
squares. Write, but do not evaluate, an integral expression for the volume of the solid.
Page 8 of 11
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