SECTION 7-3-C
More volume, washers, disks and cross
sections
6. The base of a solid is bounded by
y  x3 , y  0, and x  1.
Find the volume of the solid for each of the following cross
sections taken perpendicular to the y-axis.
(a) Squares
6. The base of a solid is bounded by
y  x3 , y  0, and x  1.
Find the volume of the solid for each of the following cross
sections taken perpendicular to the y-axis.
(b) Semicircles
6. The base of a solid is bounded by
y  x3 , y  0, and x  1.
Find the volume of the solid for each of the following cross
sections taken perpendicular to the y-axis.
(c) Equilateral triangles
7. (2004 Form B)
Let R be the region enclosed by the graph of y  x  1
the vertical line x = 10, and the x-axis.
(a) Find the area of R.
7. (2004 Form B)
Let R be the region enclosed by the graph of y  x  1
the vertical line x = 10, and the x-axis.
(b) Find the volume of the solid generated when R
is revolved about the horizontal line y = 3.
7. (2004 Form B)
Let R be the region enclosed by the graph of y  x  1
the vertical line x = 10, and the x-axis.
(c) The region R is the base of a solid. For this
solid, the cross sections perpendicular to the xaxis are equilateral triangles. Find the volume of
this solid.
8. (2003) Let R be the shaded region bounded by the
graphs of y  x and y  e 3 x and
the vertical line x = 1,as shown.
(a) Find the area of R.
8. (2003) Let R be the shaded region bounded by the
graphs of y  x and y  e 3 x and
the vertical line x = 1,as shown.
(b) Find the volume of the solid generated when R is
revolved about the horizontal line y = -1.
8. (2003) Let R be the shaded region bounded by the
graphs of y  x and y  e 3 x and
the vertical line x = 1,as shown.
(c) The region R is the base of a solid. For this solid,
each cross section perpendicular to the x-axis is a
rectangle whose height is 5 times the length of its base in
region R. Find the volume of this solid.
Assignment
Worksheet 7-3-C