All Questions
Tagged with solid-of-revolution centroid
7
questions
5
votes
1
answer
334
views
Pappus centroid theorem and Hypercones.
The volume of a straight cone in $\mathbb R^3$ is usually find adding the circular sections orthogonal to the height. If the base has radius $R$ and the height is $h$ we have:
$$
V_{C3}=\int_0^h \pi r^...
- 63.1k
0
votes
2
answers
278
views
Centroid of volume of revolution
Consider a solid generated by the curve $y^2 =ax^2+2bx+c$,rotated about the $x$-axis, and two plane surfaces at right angles to the latter, distance $h$ apart, and with areas $A$ and $B$. To prove ...
- 441
2
votes
0
answers
659
views
Finding centroid's coordinates using Pappus theorem
The task is to find the centroid of the given triangle (see the image above). We also should use the fact that the volume of a cone of radius $r$ and height $h$ is $V = \frac{1}{3}\Pi r^2h$. My ...
- 21
1
vote
0
answers
62
views
Need help with an unusual surface area
I’ve developed a 3D rendering program for bodies of non-spherical revolution, by which I mean that as the curve is rotated about the vertical axis it is modulated by an arbitrary closed curve. ...
- 7,778
1
vote
1
answer
343
views
What is the volume of a solid S obtained when a region R is rotated about the line y=2x?
Alternate method using multivar also displayed
Let R be the region in the first quadrant bounded by the line $y=2x$, the curve $y=sin(x)$, and the line $l$ that is perpendicular to $y=2x$ and goes ...
- 13
0
votes
3
answers
8k
views
Centroid of a solid of revolution
I am trying to calculate the centroid of the solid of revolution defined by $y=\sin (x)$ from $x=0$ to $x=\pi$ rotated around the $x$ axis. All the information I've been able to find online relates ...
- 11
1
vote
1
answer
3k
views
Pappus's Centroid Theorem
Pappus's Centroid Theorem may refer to one of two theorems.
Theorem 1:
The surface area of a solid of revolution is the arc length of the generating curve multiplied by the distance traveled by the ...
- 3,405