# Questions tagged [solid-of-revolution]

This tag is for questions regarding to "Solid of revolution", a three-dimensional object obtained by rotating a function in the plane about a line in the plane.

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### Formalize an observation about centroid of solid of revolution

Let's suppose to have a figure $\Bbb F$ on the plane –to simplify– $(y, z)$; and to revolve it of an angle $\alpha$ about $(z)$-axis. Sometimes it happens that it's not needed to evaluate explicitely ...
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### Solid defined in 3 dimensions [closed]

Which shape is defined as follows: $A=\{ (x,y,z) \in \Bbb{R}^3 : 0\le{y}\le{1}, 0\le{z}\le{1}, z\le{x}\le{z+1}\}$ I struggle picturing these things.
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### Intersection of a line with a specific surface of revolution

As part of an art project, I'm trying to write a program to raytrace eggs, as defined by the model described in this paper. As part of writing this program, I am trying to calculate the intersection ...
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### 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 ...
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### Find the length of the barrel and the greatest and least values of the diameter.

The shape of a barrel is made by rotating the segment of the curve $y=40-0.002x^2$ between $x=50$ and $x=-50$, around the x-axis. The units are in centimeters. What is the length of the barrel and ...
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### What is the 2D shape that gives the maximum finite volume of a solid of revolution?

What is the 2D shape that gives the maximum finite volume of a solid of revolution? The following image (inspired by the one at Weisstein, Eric W. "Pappus's Centroid Theorem." From MathWorld-...
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### Finding the height of a Pyramid where the sides are given by an equation

Problem: The vertex of a pyramid lies at the origin, and the base is perpendicular to the x-axis at $x = 4$. The cross sections of the pyramid perpendicular to the x-axis are squares whose diagonals ...
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### Find volume of the solid generated by revolving

Find volume of the solid generated by revolving the region bounded by the parabola $𝑥=𝑦^2+1 ,𝑦=0$ and the line 𝑥=3 about the line 𝑥=3 Using Disk method,I found the answer to be 9.4
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### Find the function $f(x)$ knowing the volumen of the solid of revolution for $a \gt 1$

Find the function $f(x)$ knowing that the volumen of the solid of revolution of $y=f(x)$ around the x axis, for $a \gt 1$ is $V=a^2 -a$ , $f(x)$ continuos and $f(x) \gt 0$ Basically what I tried to ...
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