Volumes of Solids Worksheet. For the shaded region R in each figure, find the following: REGION I a) The area of R b) The volume when R is rotated abo...
Volumes of Solids Worksheet For the shaded region R in each figure, find the following: REGION I a) The area of R b) The volume when R is rotated about the x-axis. c) The volume when R is rotated about the y-axis. d) The volume when R is rotated about the line x = -2. e) The volume when R is rotated about the line y = 6. f) The volume when R is the base of a solid and the cross-section of this solid are rectangles perpendicular to the x-axis with the base twice as long as the height.
y=x2
x=± y (2,4)
(0,0)
y=4x-x2
x = ± 4− y +2
Page 1 of 3
More Area and Volume
REGION 2 a) The area of R b) The volume when R is rotated about the y-axis. c) The volume when R is rotated about the line x = 4. d) The volume when R is rotated about the line x = -7. e) The volume when R is the base of a solid and the cross-section of this solid are semicircles perpendicular to the x-axis.
y=x-2 x=y+2 (4,2)
(1. –1)
x=y2 y=± x
Page 2 of 3
More Area and Volume
REGION 3 a) The area of R b) The volume when R is rotated about the x-axis. c) The volume when R is rotated about the line y = 9. d) The volume when R is rotated about the line y = -3. e) The volume when R is the base of a solid and the cross-section of this solid are right isosceles triangles with one leg perpendicular to the x-axis.
