- #1

- 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]

---------------------------------------------------------------

## 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.

Last edited: