# Questions tagged [solid-of-revolution]

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### Question about using Washer method

I want to use the Washer method of integration to find the volume of material in a paraboloid of thickness 0.5mm. For the Washer equation $$V= π∫b[f(x)^2−g(x)^2]dx$$ $f(x)$ is a parabola, and I know ...
2answers
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### Solid of revolution for area bounded by parabolas

Show that the volume generated by revolving the region in the first quadrant bounded by the parabolas $y^{2} =x$, $y^{2}= 8x, x^{2}= y, x^{2}= 8y$ about the x axis is $279 \pi /2$ This problem is to ...
0answers
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### Setting up integrals for calculating the volume of a solid of revolution

Set up integrals (do not solve them) for finding the volume of the solid formed by revolving the region bounded by $y=(x-1)^2 +\frac{7}{4}$ and $y=-(x+1)^2 +\frac{47}{4}$ about: $A) y=-1$ $B)x=2$ ...
1answer
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### What side of the axes to compute in a solid of revolution question and how to model a question

I'm a bit confused regarding questions involving solids of revolution. For example, a question involves a polynomal, say, $x^2+2$ is rotated about the y-axis, find the volume for the solid of ...
2answers
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### Finding the surface area of a region which is generated by revolving a curve around a line

The following problem is from the book, Calculus and Analytical Geometer by Thomas and Finney. It is early on in the book so I would expect / hope any integral would be easy to solve. Problem: Find ...
3answers
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### Solid of revolution for given area

Find the volume of the solid obtained by revolving the area enclosed by the curve $27ay^{2} = 4(x-2a)^{3} , x$ axis and parabola $y^{2} = 4ax$ about the $x$ axis. I am not able to find the area ...
1answer
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### Volume of the solid generated by revolution of the given curve.

The volume obtained on revolving about $x=a/2$, the area enclosed between the curves $xy^{2} = a^{2}(a-x)$ and $(a-x)y^{2} = a^{2}x$ is ......$?$ I've drawn both curves and both intersect at $x=a/2$, ...
1answer
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### Confusion related to the volume of a solid of revolution

Well, I've done several excercises about calculating the volume of a solid of revolution some time ago and I don't remember how I got the results of some of them. The first says "Find the volume of ...
4answers
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### Why is the slope a part of the area of a surface of revolution?

I have previously learned about the volume of a solid of revolution about the x axis and that equation makes sense to me since it's taking the integral between points a and b of the area of a circle ...
0answers
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### Finding a value to calculate volume and area using integrals

Given $D=[{(x;y) \in \mathbb R^2 : 1 \le y \le ax^2 +1, 0\le x \le 2/a}], 0 \lt a$, let $W$ be the region obtained by rotating $D$ around $Y$ axis. A) Find the volume of $W$ B) Find, if possible, ...
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1answer
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1answer
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### cross section of torus

Is there any particular name for the plane revolved about an external axis to form a torus? I was thinking of "cross section," but that could be taken as a vertical plane cutting the whole torus in ...