- #1
bob29
- 18
- 0
Homework Statement
Find the volume of the solid bounded by the paraboloids z=x^2+y^2 and z=36-x^2-y^2.
Answer is:
[tex]
324\pi
\\[/tex]
Homework Equations
r^2=x^2+y^2
x=rcos0
y=rcos0
The Attempt at a Solution
36-x^2+y^2=x^2+y^2\\
36=2x^2+2y^2
18=x^2+y^2
r^2=18
[tex]
V=\int_{0}^{2\pi} \int_0^{3\sqrt{2}} \int_{r^2}^{36-r^2} \left (1) \right dz.rdr.d\theta
[/tex]
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Homework Statement
Use cylindrical coordinates to find the volume of inside the region cut from the sphere x^2+y^2+z^2=36 by the cylinder x^2+y^2=4.
Ans is:
[tex]
\frac{4\pi}{3}(216-32^{3/2})
[/tex]
The Attempt at a Solution
Diagram is of a sphere where a cylinder is inside of it.
x^2+y^2+z^2=4
r^2+z^2=4
[tex]
z=\sqrt{4-r^2}\\
[/tex]
x^2+y^2=4
r^2=2^2
r=2
[tex]
V=\int_{0}^{2\pi} \int_0^2 \int_{-\sqrt{36-r^2}}^{\sqrt{4-r^2}} \left (1) \right dz.rdr.d\theta
[/tex]
Studying for an exam and would appreciate the help to answering these questions that I am struggling on.
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