- #1
johnhuntsman
- 76
- 0
Find the volume of the solid obtained by rotating the region bounded by the curves:
x = 2 sqrt(y), x = 0, y = 9; about the y-axis
I have this graphed and everything so I'm not sure there's a need to worry about that.
Setup (integrating with respect to y):
Outer radius = x = 2 sqrt(y). Inner radius = x = 0. Bounded by y = 9 and 0.
9
∫π[2 sqrt(y)]^2 dy
0
Which is equivalent to:
_______9
(2πy^2)| = 36π
_______0
However, my book says the answer is 162π. What am I doing wrong?
x = 2 sqrt(y), x = 0, y = 9; about the y-axis
I have this graphed and everything so I'm not sure there's a need to worry about that.
Setup (integrating with respect to y):
Outer radius = x = 2 sqrt(y). Inner radius = x = 0. Bounded by y = 9 and 0.
9
∫π[2 sqrt(y)]^2 dy
0
Which is equivalent to:
_______9
(2πy^2)| = 36π
_______0
However, my book says the answer is 162π. What am I doing wrong?