0
votes
0answers
20 views

Volume of Solid of Revolution

This problem is giving me some trouble: The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. x = (y − 5)^2, x = 4; ...
0
votes
0answers
37 views

Compute the volume of a solid

I've solved this exercise and my answer contradicts the one in the back of the book. It might be a misprint but I need to be sure. The book is Apostol's Calculus vol. 1. The book says $16\sqrt3/3$, my ...
2
votes
1answer
125 views

Disk and washer problem

I need to find the volume of the solid obtained by rotating the region bounded by the following functions: $xy = 1, y = 0, x = 1, x = 2;$ about $x = -1$ I think the outer radius of the washer is ...
5
votes
1answer
207 views

Volume of a sphere with three holes drilled in it.

Suppose that the sphere $x^2+y^2+z^2=9$ has three holes of radius $1$ drilled through it. One down the $z$-axis, one along the $x$-axis, and one along the $y$-axis. What is the volume of the resulting ...
3
votes
1answer
1k views

Volume from revolving $e^x$ around $y$-axis

In school, I had a problem something like this: A region R is bounded by $x$-axis, $y$-axis, $x = 3$, and $y = e^x$. What is the volume of the solid produced by revolving it around the $y$-axis. ...
1
vote
1answer
328 views

Surface area of revolution about $y$-axis in terms of $f(x)$

I need to find a formula for the surface area of a solid of revolution rotated around the $y$-axis. The curve is $f(x)=x^2$ on $[0,1]$. However, my answer must be in terms of $f$, not $f^{-1}$.
2
votes
1answer
1k views

Volume of the torus with an integral

I am stuck on the following question: Find the volume of the torus obtained by rotating the circle $(x-a)^2+y^2=b^2$, where $a>b$, around the y-axis.
2
votes
1answer
904 views

Solid of revolution about a slanted line

I just thought about this idea and I decided to work on it. After taking on a general case, which proved to be too difficult, I tried a specific case. Something simple like the curve $y_1 = x^2$ ...
7
votes
2answers
2k views

Volume of a pyramid, using an integral

I have a calculus exam tomorrow and this is a possible question. However, I don't know how to handle this question. Suppose you have 3 points in space: $p_1=(a,0,0)$, $p_2=(0,b,0)$ and $p_3=(0,0,c)$, ...