# Questions tagged [volume]

For questions related to volume, the amount of space that a substance or object occupies.

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### Find the volume of the given solid

Find the volume of the solid $$\{(x,y,z) : x ≥0,y ≥0,z ≥0,z ≤2 −e^y, x + y + z ≤10\}.$$ Not sure if my workings for this is correct? Any help would be appreciated, thanks! workings
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### Calculating Failure Angle of Silo Wedge

I am working on an optimization problem, specifically calculating the lateral earth pressures on the inside of a silo wall. I have been trying to solve for the failure angle of a silo wedge based on ...
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### Largest hyperrectangle contained in an ellipsoid

I am looking for a hyperrectangle with maximum volume which is contained in an ellipsoid. My Ellipsoid is defined as $\mathcal{E}=\{x\in\mathbb{R}^n\mid x^T P x \leq c \}$, where $P>0$. For smaller ...
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### $n$-dimensional spheres and gaussian scalar fields

I'm currently reviewing some problems in Statistical Mechanics and I have come across a question that I'm struggling to resolve. Specifically, in certain parts of the study of ideal gases, the concept ...
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### What's the difference between the ellipsoid described by $\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$ vs $<1$?

I have to find the volume of the ellipsoid described by the set $E = \{(x,y,z) \in \mathbb{R}^3 |\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}<1\}$. I have a few ideas and there is a bit of ...
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