# volume's questions - English 1answer

1.773 volume questions.

### 4 Find the volume bounded by the $xy$ plane, cylinder $x^2 + y^2 = 1$ and sphere $x^2 + y^2 +z^2 = 4$ [duplicate]

2 answers, 44 views calculus multivariable-calculus volume
Find the volume bounded by the $xy$ plane, cylinder $x^2 + y^2 = 1$ and sphere $x^2 + y^2 +z^2 = 4$. I am struggling with setting up the bounds of integration. First, I will calculate the 'first-...

### 9 Volume of the intersection of ellipsoids

1 answers, 1.436 views measure-theory proof-verification volume

### 2 Explanations about the volume of a regular simplex

1 answers, 860 views volume simplex
I'm really sorry, this may sound ridiculous but I can't understand the Wikipedia explanation about the volume of regular n-dimensional simplices, here. In particular, these two sentences make no ...

### Inertia Tensor of an ellipsoid

Given is the following inertia tensor of a certain mass distribution $\rho(\vec{r})$ : $$I_{ij} = \int dV \rho(\vec{r}) \left( \vec{r}^2 \cdot \delta_{ij} - r_ir_j \right)$$ I should compute the ...

### 1 Second Method to Find the Volume of a Slice of a Cone

1 answers, 40 views calculus integration volume
I was looking to formulate a general solution for a vertical slice of a cone. After failing to do this by integrating for the area of an ever shrinking chord segment, I eventually came up with a more ...

### 1 Finding radius of capsule defined by total volume and height of inner cylinder

2 answers, 44 views calculus geometry volume
I have a capsule shape that is comprised of a cylinder and two half-sphere end caps, and I want to dynamically resize it. As I stretch the capsule by increasing/decreasing the height of the cylinder, ...

### -3 Application of integrals. [closed]

2 answers, 33 views integration volume applications
What is the volume of the solid generated when the region bounded by $y=3x$ and $y=x^2 +2$ rotate about the $x$-axis ?

### 6 Volume of cannoli

2 answers, 126 views integration 3d volume
Problem statement (see pic below): 1. Wrap unit circle over cylinder with radius $r=1/\pi$, edges of unit circle will just touch each other. 2. Remove cylinder, fill cannoli with cream)). 3. Scrape ...

### Integration over a cube the correct way?

0 answers, 18 views calculus volume
Suppose we have a cube, and I want to integrate the function $f(x,y,z)$ over it where $x,y,z$ are the variable in given three dimensions. Assuming cube's center is at a distance of $d$ from the point ...

### 2 How to prove volume of parallelepiped?

2 answers, 1.740 views 3d volume
Let's say that three consecutive edges of a parallelepiped be a , b , c . Then how to show that volume is = [a b c] Or = a.(b × c) ? Also how to prove this this too?

### -1 vector bounded volume

0 answers, 12 views calculus multivariable-calculus volume
Supposing we have a point $(x_0,y_0, z_0)$ on a plane ${x^a+y^a+z^a=1}$ where $x,y$ and $z$ are positive, and a plane P which is a tangent to that point. And we need to calculate the volume of the ...

### Integrating a solid using cartesian, cylindrical and spherical coordinates

1 answers, 5.539 views integration multivariable-calculus volume
The region $W$ is the cone shown below (see image). The angle at the vertex is $π/3$, and the top is flat and at a height of $7\sqrt{3}$. Write the limits of integration for $\int_W dV$ in the ...

### 1 Volume / Surface of a Paraboloid through Integration

Given is a Paraboloid delimited as following: $$z_1 = a(x^2 + y^2),\ z_2 = h$$ That's my try for the Volume computation: First I find the radius of the circle resulting from the intersection ...

### 1 Finding the volume of an object (another)

1 answers, 30 views integration volume
T is shaped like a quarter of a donut, and can be described in cylindrical coordinates by the inequality (r−2)^2 + z^2 ≤ 1. 0≤θ≤π/2. I am asked to find the volum of T. I think you can parameterize it ...

### 1 Finding volumes through integration

I recently arrived to the chapter that focuses on finding volumes with integrals in the textbook I use. Integration is not the problem, but I've been having a very hard time solving these kind of ...

### 4 Find the volume of the solid formed by rotating about the $x$-axis

2 answers, 5.247 views calculus volume
Find the volume of the solid formed by rotating the region enclosed by the curves $y=(e^ x) + 2$, $y=0$ , $x=0$, and $x=0.7$ about the $x$-axis I set up the equations as follows using the washer ...

### 2 Volume of a sphere above a plane

1 answers, 23 views multivariable-calculus volume
I'm trying to find the volume of a region contained within a sphere centered at the origin of radius 2, and above the plane z=1. I made the computation below and just wanted another pair of eyes to ...

### Calculating the area of an irregular semi-circle

1 answers, 20 views area volume
I am very inexperienced when it comes to math and I'd like to calculate the area of an irregular semi circle. This shape is 200 ft wide and an average of 20 feet deep. (Like a wide trough shape). Any ...

### 1 Extract (maybe oblique) slice from a volume

0 answers, 17 views matrices volume
I have a three-dimensional matrix (representing a volume) with integer values in it (grey values). I now want to put a (maybe oblique) plane inside the volume and extract the values that project onto ...

### How to calculate the volume of a regular convex icosahedron?

0 answers, 31 views geometry 3d volume
I know that the volume of an icosahedron is $\frac {5(3+\sqrt{5})} {12}x^3$, where x is the length of any given side. However, I am not sure how to prove it. I have looked into a few methods, yet none ...

### Why we don't consider absolute value of volume-form for integration?

Volume form on a manifold is alternating and this lead to impossibility on integration on a non-orientable manifolds (because there is no continuous valume form on them) But if we consider absolute ...

### How do I find the volume of Solid of Revolution for this particular graph?

2 answers, 23 views volume solid-of-revolution
I've been given the graph y = $4x - 4x^2$ that has been bound by the x-axis. I've been asked to find the volume of Solid of Revolution about the y-axis using the disc method. In order to find the ...

### Triple integral - wedge shaped solid

3 answers, 1.107 views integration multivariable-calculus volume
Find the volume of of the wedge shaped solid that lies above the xy plane, below the $z=x$ plane and within the cylinder $x^2+y^2 = 4$. I'm having serious trouble picturing this. I think the z ...

### How to compute volume of intersection of non-axis-aligned cuboids in 3D?

0 answers, 21 views geometry algorithms volume
Given two cuboids in 3D space (8 vertex coordinates each) that are arbitrarily oriented, how can we find the volume of overlap between them in the fastest manner? An algorithm that one can code up ...

### Find the volume of the region bounded by the coordinate​ planes and a cylinder

The Plane: $x+y=4$ The Cylinder: $y^2+9z^2=16$ I have gone this far but I'm not sure it's true $$V=\int\limits_0^4\int\limits_0^{4-x}\int\limits_0^{\sqrt{16-y^2}/9} dz\ dy\ dx$$ PS: Answer can ...