Volumes of Solids
1. Region A is the area bounded above by the curve and below by the line y = x. Find the volume of the solid if region A is revolved around:
a) y-axis
b) x=3
c) x=-2
2. Region T is area in the first quadrant bounded above by the parabola y =x2, below by the x-axis and on the right by the line x= 2. Find the volume of the solid generated when region T is revolved around:
a) y-axis
b) x = 2
c) x = -3
3. Region R is the area in the first quadrant bounded by the functions. Find the volume of the solid if region R is revolved about the given line.
a) x-axis
b) y-axis
c) y = 12
d) y = 15
e) x = 4
1998 AB-1 The region R is bounded by the x-axis, the graph of , and the line x=4.
a) Find the area of the region R.
b) Find the value of h such that the vertical line x=h divides the region R into two regions of equal area.
c) Find the volume of the solid generated when R is revolved about the x-axis.
d) The vertical line x=k divides the region R into two regions such that when these two regions are revolved about the x-axis, they generate solids with equal volumes. Find the value of k.