Chapter 7
C1. The volume of the solid formed by revolving the region bounded by the graph of y   x  3 and the
coordinate axes about the x-axis is given by which of the following integrals?
2
3
 A     x  3
3
2
 B    x  3
dx
0
9
4
0
dx
 C     x  3
9
4
dx
0
 D  2  x  x  3
0
3
2
dx
 E  2  x  x  3
4
dx
0
C2. The region in the first quadrant enclosed by the graphs of y=x and y=2sinx is revolved about the x-axis.
The volume of the resulting solid figure is
(A) 1.895
(B)2.126
(C)5.811
(D)6.678
(E)13.355
C3. The region enclosed by the line x+y=1 and the coordinate axes is rotated about the line y=-1. What is the
volume of the solid generated?
17
17
2
3
4
( A)
( B)
(C )
( D)
(E)
2
4
3
4
3
C4. The region R enclosed by the coordinate axes and the graph of y  k  x  2  is shown below. When this
2
y
region is revolved around the y-axis, the solid formed has a volume of 8 cubic units. What is the value of k?
 A 1
 D 2
4
3
E3
 B
C 
3
y=k(x-2)2

R
x
NC 5. A solid has a circular base of radius 3. If every plane cross section perpendicular to the x-axis is an
equilateral triangle, then its volume is
( A) 36
( B)12 3
(C )18 3
( D) 24 3
( E ) 36 3
C6. The base of a solid is the region enclosed by the coordinate axes and the graph of y  3  x  2  . If every
cross section perpendicular to the x-axis is a square then the volume of the solid is
(A) 8.0
(B)19.2
(C)24.0
(D)25.6
(E)57.6
2
NC 7. The velocity of a particle moving along the y-axis is given by v(t)=8-2t for t>0. The particle moves
upward until it reaches the origin and them moves downward. The position of the particle at any time t is given
by
( A)  t 2  8t  16
( B)  t 2  8t  16
(C )2t 2  8t  16
( D)8t  2t 2
( E )8t  t 2
NC 8. A particle moves on the x-axis in such a way that its position at time t is given by x(t )  3t 5  25t 3  60t.
For what values of t is the particle moving to the left?
(A) –2<t<1 (B)-2<t<-1 and 1<t<2
(C)-1<t<1and t>2
(D) 1<t<2
(E) t<-2, -1<t<1, and t>2
NC 9. Which graph best represents the position of a particle, s(t) as a function of time, if the particle’s velocity
and acceleration are both positive?
s(t)
s(t)
s(t)
s(t)
s(t)
A
B
C
D
E
1
x
NC 10. A particle moves along the x-axis so that at any time t its position is given by (t )  sin t  cos(2t ).
2

What is the acceleration of the particle at t  ?
2
1
3
5
7
( A) 0
( B)
(C )
( D)
(E)
2
2
2
2
t
t
t
t
t