All Questions
Tagged with solid-of-revolution solid-geometry
16
questions
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Finding the equation of two lines lying on the surface of a hyperbloid
Trying to solve this question:
Surface S is obtained by revolving the line $x^2-z^2=4$ around the "z" axis.
Write the equation for S.
Show that exactly two lines pass through M=(2,0,0) ...
- 3
2
votes
0
answers
70
views
Surface (superior and lateral) and volume of an ungula
Context
Definition: An ungula is the solid obtained by cutting a cone with a plane and keeping the part between the base of the cone and the plane
I couldn't find the formulas to obtain the upper ...
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1
answer
27
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How can I estimate the volume of a solid object, knowing only it's longitudinal corss-sectional area?
Let's say the shape is too complex to split it into simpler parts and solve it analytically.
I can obtain it's longitudinal cross-sectional area by loading the image into an image editor, scaling it ...
1
vote
2
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682
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Calculate volume of solid obtained by rotating region bounded by $y=x^2$, line $y= −2$, from $x=0$ to $x=2$ around line $y=−2$. [closed]
Problem : Calculate the volume of the solid obtained by rotating the region bounded by the function $y=x^2$, the line $y= −2$, from $x=0$ to $x=2$ around the line $y=−2$.
My Attempt
Can someone guide ...
- 21
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37
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To compute the volume and the lateral area of a $3D$ tube with non-uniform section whose axis is a spatial line $L$
What's the way to compute the volume and the lateral area of a $3D$ tube with non-uniform section whose axis is a spatial line $L$? And what's the mathematical name of this geometry in the first place?...
- 11
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2
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2k
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How to get the parametric equation of a rotated cylinder (with certain slope)
I have a basic question but I have failed in solving it. I have the equation of a cylinder which is $y^2 + z^2 = r^2$ (centered in the x-axis). The parametric equation (dependent on $L$ and $s$) is $(...
- 23
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101
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Description of curve arising from rotation of a cube
Take a unit cube, and place it so that one of its body diagonals lies along the $z$-axis. For symmetry, assume that the vertices of the cube are at $(0,0,\pm\sqrt{3}/2)$. Then rotate it about the z-...
- 9,632
1
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1
answer
65
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Volume of a solid by revolution (cylindrical shells)
I frequent Stack Overflow, but I am new here. I was given this problem:
Use the method of cylindrical shells to find the volume $V$ generated by rotating the region bounded by the given curves about ...
- 43
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2
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373
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I need help with constructing a "3D" cone out of paper with precise angles.
I just can't seem to wrap my head around it. - I need to make an accurate and precise model of a cone out of paper, with it's angle around the cap/spike equal to $90^° $ - I know it seems obvious but ...
1
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43
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Medial axis of symmetric solid & volume
I have a problem and would appreciate some pointers. In short, I have a solid which is produced by revolving a 2D polyline around an axis, thus producing a solid of revolution. Now:
1) Is there some ...
- 299
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32
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Finding the volume of a right cylinder in terms of full surface area and a variable
Let S be the full surface area of a right cylinder. Let H be the height of the cylinder and r be the radius of it's base. Let m = H-r. Find the volume V of the cylinder in terms of S and m.
- 108
2
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3
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1k
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If I have an oblique cylinder can I trim it in to a rectilinear cylinder?
There was an interesting conversation on twitter today about the net of an oblique cylinder. I misunderstood the question and produced a net of a right cylinder sliced by a plane with the equation $ax+...
- 6,268
4
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2
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2k
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Surface Area of a Lemon
I'm a high school senior doing the AP Calc course, and recently I studied surface area of revolutions. As background research for a class project, I tried to look for things found in nature that ...
- 165
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1
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1k
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What is the implicit equation $F(x,y,z) = 0$ for this non-standard torus?
I was reviewing an old material on 3D surfaces from my college days. As an exercise, I am trying to write an implicit equation for a torus like manifold.
While it is relatively straight forward to ...
- 1,042
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Theorems on toric sections
Do any theorems other than Villarceau's theorem and closely related results say anything about intersections of planes with tori?
