All Questions
Tagged with solid-of-revolution parametric
6
questions
3
votes
1
answer
244
views
How to find the function of a surface
Let’s say we have $f(x)=\sqrt{x}$ in range $\,x\in[0,5]\,$ and we revolved around the $x$-axis what would the function $z=z(x,y)$ of this new surface? How can I find this surface?
I have the volume of ...
- 1,043
3
votes
2
answers
64
views
Is there a way to modify the solid of revolution integral to allow for solids of increasing and decreasing radius?
I am doing a project on tori as they relate to pool floaties and the volume of a normal torus can be calculated by the solids of revolution integral on a circle, Is there a way to modify the integral ...
- 33
2
votes
1
answer
275
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On Surfaces of Revolution With Any Two Relations in $\Bbb R^2$ Such that One is the Axis (g) and the Other Revolves (f) defined by z=Rev[f(x),g(x)]:
For the last few years, I have tried a couple times to solve this problem that I came up with. Even though this may seem like a nonsensical idea, there is still a seed of wonder embedded into it.
This ...
- 12.5k
1
vote
0
answers
73
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Limits for the parameters of the parametric equation of a surface of revolution
According to Lipschutz's Differential Geometry book,
A surface of revolution $S$ is obtained by revolving a plane curve $C$ (the profile curve) about a line $L$ (the axis of $S$) in its plane. If $x_{...
- 801
1
vote
2
answers
150
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Find the area of the surface formed by revolving the given curve about $(i)x$-axis and $(i)y$-axis
Q:Find the area of the surface formed by revolving the given curve about $(i)x-axis$ and $(i)y-axis$
$$x=a\cos\theta ,y=b\sin\theta,0\le\theta\le2\pi$$
About $x-$axis is, $S=2\pi\int_0^{2\pi}b\sin\...
- 161
2
votes
1
answer
2k
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Surface Area of Revolution around y=x
Consider the curve $x=-t^2$ , $y=\frac{t^3}{3}-t+1$ , $t\in[0,1]$. Find the surface area obtained by revolving the curve about the line $y=x$.
On my textbook there are formulas to find the surface ...
- 169