It is currently Fri Aug 23, 2019 3:24 pm

 All times are UTC [ DST ]

 Print view Previous topic | Next topic
Author Message Posted: Wed Dec 13, 2017 10:34 pm

Joined: Wed Nov 15, 2017 12:37 pm
Posts: 20
Can you help me calculate the mass of the solid bounded by the surfaces $x^2+y^2=2y$ and $z=\sqrt{x^2+y^2}$ given its density function $m(x,y,z)=\sqrt{x^2+y^2}$ ?

Top    Posted: Fri Dec 15, 2017 6:32 am
 Team Member Joined: Mon Nov 09, 2015 1:36 am
Posts: 460
Location: Ioannina, Greece
andrew.tzeva wrote:
...the solid bounded by the surfaces $x^2+y^2=2y$ and $z=\sqrt{x^2+y^2}$ ...

The solid isn't well defined. The surface $x^2+y^2=2y$ is a cylinder and the surface $z=\sqrt{x^2+y^2}$ is the "upper" half of the double cone $z^2=x^2+y^2$. These two surfaces does not enclose a solid. (See figure)
Attachment: On the other hand, the double cone $z^2=x^2+y^2$ and the cylinder $x^2+y^2=2y$ enclose a solid. Maybe this is the case...

_________________
Grigorios Kostakos

Top    Posted: Sun Dec 17, 2017 12:27 pm

Joined: Wed Nov 15, 2017 12:37 pm
Posts: 20
Is there a general rule to solve this kind of problems, given two surfaces that bound a solid and its density function ?

Top    Posted: Sun Dec 17, 2017 3:51 pm
 Team Member Joined: Mon Nov 09, 2015 1:36 am
Posts: 460
Location: Ioannina, Greece
andrew.tzeva wrote:
Is there a general rule to solve this kind of problems, given two surfaces that bound a solid and its density function ?
Yes, there is a general formula to calculate the mass of a solid $S$ with given density function $f:S\subset\mathbb{R}^3\longrightarrow\mathbb{R}$ :
$\displaystyle\mathop{\iiint}\limits_{S}{f\, dS}\,.$

_________________
Grigorios Kostakos

Top    Posted: Mon Dec 18, 2017 2:29 pm

Joined: Wed Nov 15, 2017 12:37 pm
Posts: 20
Thank you!

Top   Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending

 All times are UTC [ DST ]

#### Mathimatikoi Online

Users browsing this forum: No registered users and 0 guests

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

Search for:
 Jump to:  Select a forum ------------------ Algebra    Linear Algebra    Algebraic Structures    Homological Algebra Analysis    Real Analysis    Complex Analysis    Calculus    Multivariate Calculus    Functional Analysis    Measure and Integration Theory Geometry    Euclidean Geometry    Analytic Geometry    Projective Geometry, Solid Geometry    Differential Geometry Topology    General Topology    Algebraic Topology Category theory Algebraic Geometry Number theory Differential Equations    ODE    PDE Probability & Statistics Combinatorics General Mathematics Foundation Competitions Archives LaTeX    LaTeX & Mathjax    LaTeX code testings Meta Powered by phpBB® Forum Software © phpBB Group Color scheme created with Colorize It.
Theme created StylerBB.net