# 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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### What software can I use to graph a solid of revolution between 2 functions?

What software is used to graph solids of revolution between 2 functions like the ones below?
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### Find the volume of y=(x^2)/8, x=2, y=0 about line x=-2 [closed]

Use disk/washer method to evaluate from 0 to 1/2
1 vote
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### Find the volume of the solid generated by revolving the region enclosed by $y=x^3$ and $y=x$ about $x$-axis.

I need help with this exercise. Find the volume of the solid generated by revolving the region enclosed by $y=x^3$ and $y=x$ about $x$-axis. When I graph I get that these are the enclosed regions: If ...
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1 vote
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### Calculating Volume of Solids Rotated About y-axis and line

I have the following two "calculate the volume of the solid obtained by rotating the region" questions. Let $y = 2 - x^2$ and $y = x^4 - x^2$, and let $R$ denote the region bounded by the ...
• 205
1 vote
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### Volume generated by rotating axis $X =2$ and the lines $x =0$ and $y = 1$

The question I wrote the shaded area equation and add 2 to it because it has shifted two units to the right, however the answer is wrong, where did I go wrong?
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### Finding the exact volume of a solid with y=5sqrtx, x=0, y=6

I just started Calculus 2 recently and while things were running smoothly, I am having trouble with volumes. At first I tried with this question the Vertical Revolution formula: 2π 0to6 (bounds) (...
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### Setting up an integral that represents the volume using Washer/Shell method

Let A be the region in the first quadrant bounded by the curve $y=\cos x$, the line tangent to $y=\cos x$ when $x=\frac{\pi}{4}$ and the y-axis. a) We now rotate A with respect to the line $y=-1$. Set ...
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### Find the volume of the solid of revolution formed when the region bounded by $y=\sqrt{\frac{x-1}{x^3}}$ and $y=0$ is revolved about the $x$-axis

Image description here The question is : Analytically find the volume of the solid of revolution formed when the region bounded by $y=\sqrt{\frac{x-1}{x^3}}$ and $y=0$ is revolved about the $x$-axis ...
1 vote
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### How to Minimize the surface area of a solid of revolution of a constant volume?

I read this post here however, I want to know whether it would be possible to minimize the surface area of a solid of revolution which is a non catenary. Catenary curve for minimum surface of ...
1 vote
33 views

### Surface area of cone by integration, $\pi rh$ instead of $\pi rl$

I was trying to derive the formula for the surface area of the curved part of a cone, but ran into a problem. Let $f(x)=kx$ be any line with any angle passing through the origin, $h$ be the height (...
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### Find the volume of the solid obtained by rotating the region 𝐴 in the figure about 𝑥=3.

I am stuck with this problem given that $a=3$ and $b=6.$ I was trying to cut with respect to $y$. I tried to do two integrals: from 0 to 6 and 6 to 15 because $y = 9+6$. However, I think my integral ...
1 vote
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### Volume of $2$ Solids of Revolution

The region bounded by $x = y^{2}$ and $x = 2-y^{2}$, revolved around the line $x = 3$. By using the Washer method, I acquire: $$\pi \int_{-1}^{1} (y^2)^2 - (1-y^2)^2 \space dy$$ However after ...
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1 vote
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