# Questions tagged [volume]

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

2,024 questions
0answers
18 views

1answer
17 views

### How can I find the volume generated by revolving the following region about $x=5$?

The region enclosed by : $y=6-x^2$ and $y=5$ I first get the inverse functions and the intersections and then work with the disk/washer method, the result is zero and I can't figure out what am I ...
1answer
24 views

### Volume of a solid $y=\cos(x)$ and $y=0$ for the interval $0\le x \le \frac{\pi}2$

Volume of a solid $y=\cos(x)$ and $y=0$ for the interval $0\le x \le \frac{\pi}2$. I used method of shells to get: $$2\pi\int_{0}^{\pi/2}x\cos(x)\,dx.$$ And I got: \begin{align} 2\pi\int_{0}^{\...
1answer
28 views

### Volume of surface Revolution by area bounded by $y=\sin(x)$ and $y=0$

The revolution across the y-axis, and the bounded area is between $y=\sin(x)$, and $y=0$ for ${0\le x \le \pi}$. I did: $$V_{shells}= 2 \pi \int_\limits{0}^\pi x\sin(x)dx=2\pi^2$$ I am trying to do ...
2answers
26 views

### Volume of the pyramid - how to find the coordinates of 4 vertices?

The pyramid is bounded by planes: $x=0$, $y=0$, $z=0$ and $9x-y-3z=54$. IT is needed to calculate the volume $V=\frac {1} {3} bh$, where where $b$ is the area of the base and $h$ the height from the ...
0answers
35 views

### Triple integral to calculate the volume of pyramid vs it's formula

It is well known the formula to calculate the volume of a pyramid: $V=\frac {1} {3} bh$, where where $b$ is the area of the base and $h$ the height from the base to the apex. However I need to ...
1answer
68 views

### Maximum volume cylinder from a sheet of paper

We have an A4 sheet of paper and we have to build a cylinder of maximum volume using this paper by cutting out a rectangle and the two base circles in order to make the construction. My approach: ...
1answer
37 views

0answers
20 views

0answers
40 views