Volumes Math Worksheet 6.3 With Answers Page 9
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11Calculus Maximus
WS 6.3: Volumes
12. (AP 2008-1) (Calculator Permitted) Let R be the region bounded by the graphs of
y
sin
x and
3
y
x
4
x , as shown in the figure.
(a) Find the area of R.
(b) The horizontal line
y
2
splits the region R into two parts. Write, but do not evaluate, and
integral expression for the area of the part of R that is below this horizontal line.
(c) The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a
square. Find the volume of this solid.
(d) The region R models the surface of a small pond. At all points in R at a distance x from the y-axis,
the depth of the water is given by
h x
3
x . Find the volume of water in the pond.
Page 9 of 11
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