All Questions
8
questions
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45
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Cavalieri's Principle in volume calculation
In petroleum engineering, for easier calculation of the volume underlying a specific surface underground, the irregular surfaces are modeled by an equivalent surface with circular cross sections, ...
0
votes
1
answer
109
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Help with volume integration application problem using Disk or Washer Methods, revolving about x-axis, revolving about y-axis.
I need to find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines: y = $\sqrt {x}$ $y=0$, and $x=3$. A) the $x-axis$ B) the $y-...
- 1
1
vote
1
answer
686
views
what is the volume generated by rotating the given region.
My professor says the volume generated by rotating the region $\mathscr{R}_2$ about the line $OA$ is $5/\pi$ but I don't see how that could be the answer?
- 107
2
votes
2
answers
225
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Volume of a circle $x^2 +y^2 \leq 1$ which is revolving around a line $x+y=2$.
I want to compute the volume of a circle $x^2 +y^2 \leq 1$ which is revolving around a line $x+y=2$. Usually I solved problems about solids revolving around axis and non axis horizontal and vertical ...
0
votes
1
answer
57
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Find the volume obtained by totating the area formed by $y=x$ and $y=\sqrt{x}$ about $y=1$
The questions asks us to find the volume of solid formed when the area between $y=x$ and $y=\sqrt{x}$ is rotated about the line $y=1$.
I understand that a cone is formed. Now, to find the volume, I ...
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2
votes
4
answers
1k
views
How does Volume work with integration?
Using a cross section suppose, as described here: Area formula Paul Notes
Suppose this is: $y = f(x)$.
He says the volume is:
$$\int_{a}^{b} A(x) dx$$
But how does area over that interval give ...
- 11.2k
0
votes
1
answer
4k
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Using differentials with volume of a cube
My question is
The volume of a cube is increased from $1000$ cubic centimeters to $1156$ cubic centimeters.
Use differentials to determine. the side length of the cube increases by? the surface area ...
- 121
3
votes
1
answer
227
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Ancient calculus or thorough observation
Integration. It's the simplest way on earth with which we can derive any formula like surface area or volume of symmetrical shapes and solids (square, circle, cube etc.). But what I've been hearing is ...
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