Let R Be the Region Bounded by the X-Axis, the Graph of , and the Line X=4

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.