# 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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### Graphing rational expressions of trig/exp by hand?

In my math class, we are not allowed to use calculators. Thus, when I see problems with an exponent/log or trig either in top or bottom and I have to graph them to solve the problem, I'm not sure ...
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### How do you express a surface of revolution as the graph of a function?

Consider a real function $f$ with domain non-negative real numbers. Let $y = f(x)$, and consider the surface traced out by rotating the graph of $f$ about the $y$-axis. This surface is the graph of ...
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### What is the correct formula for the washer method?

Almost everywhere I look the formula is: $$\pi \int_b^a {\left(f(x)^2 - g(x)^2\right) dx}$$ where f(x) is the big function and g(x) is the smaller function. Though I've run into problems while ...
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### Washer method, axis intersecting with region itself

I know the basic idea of disc / washer / cylindrical shell methods, to find the volume of solids generated : be it a single function, or the bounded region between two functions. The trouble I am not ...
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### Solid of revolution problem - clepsydra (water clock)

I need help to understand this problem: A clepsydra, or water clock, is a glass container with a small hole in the bottom through which water can flow. The "clock" is calibrated for ...
### Finding the volume of revolution obtained by rotation of a region about the line $2x-y=20$
I have the following question before me: Find the volume of the area bounded by the curves $y=x^3$, $x+y=10$ and $x=0$ about the line $2x-y=20$. I started off by drawing the given area and line of ...