All Questions
Tagged with solid-of-revolution solution-verification
10
questions
2
votes
0
answers
57
views
Finding Volume of Revolution Given by $y = \sin x$
The question given is to find the volume of revolution generated by the graph of $y = \sin x$ on the interval $[0, \pi]$.
The way I attempted was to form the sums of cylindrical segments given by $\...
- 1,467
0
votes
1
answer
45
views
Volume around $y$ axis
To find the volume of the solid of revolution around $y$ bounded by
$$y=x^2,\quad y=x-2$$
and the lines $y=0$ and $y=1$, I did as follows: since the region is
Then, the volume is:
$$2\pi\cdot\left(\...
- 2,084
2
votes
0
answers
70
views
Surface (superior and lateral) and volume of an ungula
Context
Definition: An ungula is the solid obtained by cutting a cone with a plane and keeping the part between the base of the cone and the plane
I couldn't find the formulas to obtain the upper ...
0
votes
0
answers
71
views
Volume of the solid of revolution: $y=x^2$ about $y=x$.
Question: The region bounded by $y=x^2$ and $y=x$ is rotated about $y=x$. Find the volume of the solid of the revolution.
My answer: I rotated the region $45^\circ$ clockwise and obtained the curve $(...
- 11.9k
1
vote
0
answers
73
views
Integral of volume of a solid of revolution
Hello! I was practicing for my upcoming math test, but I wasn't sure about this problem. I think I did it right, but I just wanted to check to be safe. I got answer choice B. Would anyone know if that ...
- 21
1
vote
1
answer
261
views
What's wrong with my Surface Area of a solid of revolution formula?
When I learnt about the derivation for the formula $$V=\pi\int_{x_1}^{x_2} y^2~dx$$
where $V$ is volume of the solid generated when $y=f(x)$ is rotated about the $x$ axis by $2\pi$ radians between $...
- 6,560
1
vote
2
answers
66
views
Shell method to compute volume
I'm currently learning about the shell method to compute the volume of a solid of revolution. I am working on the following problem:
Find the volume of the solid obtained by rotating the region by $y =...
user865969
2
votes
0
answers
49
views
Finding a volume generated by a parabola
Below is a problem I did. The book gets $\frac{16\pi}{15}$.This number seems to large to me. I am hoping that somebody can confirm that I got it right or tell me where I went wrong.
Problem:
Find the ...
- 4,064
0
votes
1
answer
293
views
If the region $D$ is revolved about the $z$-axis in $ℝ^3$, then the volume of the resulting solid is
Consider the region $D$ in the $yz$ plane bounded by the line $y=\frac{1}{2}$ and the curve $y^2+z^2=1$, where $y\geq 0$. If the region $D$ is revolved about the $z$-axis in $ℝ^3$, then the volume of ...
- 642
0
votes
1
answer
42
views
Calculating the volume soild of revolution made with a function and its tangent
A tangent of the curve $y=\sqrt{x}$ at point Q crosses the point P(-1,0). What is the volume of the solid of revolution when the area bounded by the line PQ, $y=\sqrt{x}$ and the x-axis is rotated ...
- 75