# volumes

1. ### Volumes of revolution problem: Where did I go wrong?

The picture shown below shows two problems. I attempted to solve the one on the left, but the answer I received does not match the answer in the back of the textbook. I would like to know where I went wrong when attempting to solve this problem. 1. Using the values shown, I created the...
2. ### Cone and conical frustum volumes correlation?

With my high school math skills I can't budge much more than this on the top of my head so... Given a cone (see picture), if we slice it horizontally a certain amount of times, we get many conical frustums and finally a cone on top. For simplicity I divided it just in 3 volumes, and I...
3. ### Volumes of Solid Regions

Could someone help me out with this problem: Set up an iterated integral representing the volume of the solid region inside the parabolic cylinder y = x2, bounded by the plane z = y + 2, the plane z = y - 2, and the plane y = 1. What I know is that you use a double integral with h(x)-g(x) as the...
4. ### Does center of mass of symmetrical figure split figure into equal volumes?

The question is as follows: a: Find the center of mass of a solid of constant density bounded below by the paraboloid z^2 =x^2 + y^2 and above by the plane z=4 b. Find the plane, z=c, that divides the solid into two parts of equal volume. This plane does not pass through the center of mass...
5. ### Volume of a Solid

I'm having trouble with this unit and have one question (#1). I'm sure I can figure out the rest once I get some help, thank you! I've also attached my set-up so far. The quarter circle is confusing me: x^2 + y^2 = 9 y = (sqrt(5)/2)x x = 0
6. ### volumes of revolutions (parametric)

How can i find the volume of a tear drop curve with the parametric equations of x(t)=cos(t) and y(t)= sin(t)sin^2(t/2), with limits from -1 to 1 using the disk method (intg(lower, upper limit) (y)^2(dx/dt)dt). I would also like to know how i can justify these equations that make the tear drop...
7. ### Liquid Volumes

"A bottle with a bowl shaped like hemisphere of diameter 8 cm contains 80mL of water, 20mL of powerade, and two ice-spheres, each with a diameter of 2 cm. What is the depth of the liquid?" How I would start the problem is attached: I'm not sure if what I did was correct though. I would...
8. ### Comparing volumes in 8 dimensions

Hello, I have an 8-dimensional convex hull which I want to approximate by a hyper-ellipsoid. When I project the convex hull into any 2 dimensions, the convex hull projection has a greater area than the projection of the hyper-ellipsoid. However, when I calculate the volume of the 8-dimensional...
9. ### Volumes by cylindrical shells

Hello, I am supposed to use the method of cylindrical shells to find the volume of the following: y=4x-x^2, y=3 about x=1 The correct answer proposed by the book is \frac{8/pi}{3} but I keep getting 2 times that. Where did I go wrong? Thank you. -Sakon Edit: I think my error is that the...
10. ### Volumes by cylindrical shells

Hey, In question #1, why is the radius x ? Should it not be (2+x) because we are rotating it around the x=0 and the curve starts at x=2, and ends at x=4? In question 2 , why isn't the function (2- \sqrt{1+x^2} , top most function - bottom function = ?? ?and I am getting 8pi/3 as an answer...
11. ### Volumes by cylindrical shells

Hello, can someone tell me where I went wrong with trying to find the volume using the shells methode? I get the correct answer using the disk method (5 pi / 14). Thank you!
12. ### Calculus III: defining volumes using spherical and cylindrical coordinates.

Hi, I need help doing these questions, I'm having trouble with defining the domain of this solid: http://imgur.com/WsqIV5G . So far I've gathered that the (r,z) graph should look like a circle of radius sqrt(2) (for the sphere part) intersected by a line at r = 1 (the cylinder) and shaded in...
13. ### volumes -cylinder and planes.-for upcoming exam

Hello, how should I solve this problem.thanks. ∫∫∫(2x+z)dv,where v is the region bounded by the cylinder x²+y²=4 and the planes x=0,y=0,z=0 and z=3
14. ### Math C Question on 'Volumes of Revolution'

Ok so I have the two coordinates (0,3) and (2,7) The line that runs through them is y=2x+3 How do I find the volume created by rotating the line around the x axis.. In other words, I will be using volumes of revolution. However, I have only bee taught on this how to just find the volume of a...
15. ### Volumes of revolution

A region is bounded by the given curves. Find the volume of the solid of revolution obtained by rotating the region about the -axis. (give your answer in terms of or approximated to the nearest tenth). y=3x x=1 x=2 x axis. Im having alot of trouble with this assignment because I just dont...
16. ### In need of verification and help, integration of volumes

Hi. I am not sure if these questions have been posted before. Reworked them today, the answers are not in the book: Find volume generated by revolving the regions bounded by given curves about y axis Question 26-3-20 y^2 = x, y = 4, x = 0, Disks Attempt: dV = pix^2 x^2=y^4 Integration...
17. ### Volumes Of Revolution

For (i) could I say to revolve the region at x = 1? Would that be a plausible answer? I'm sorry I'm confused.... Is the reason that they're talking about the place where you revolve the shape?
18. ### Volumes of Revolution

Having a bit of trouble with this one. Can anyone help me out? Many thanks. Q. The given diagram (see attachment) shows the line y=2x. Find the volume generated when this line is rotated about the x-axis from x=3 to x=0 Attempt: If x=3, the height of the generated volume is also 3. For x=3...
19. ### Help with Volumes

I asked two different people and one person got 256/9 by taking parabolic slices, and another person got 8*pi by taking slices that are circles. Who is right and why?
20. ### Volumes of revolution

Hello all, New here but needing some help on a few questions in involving areas no in the first quadrant. Question 1: Find the volume of the solid generated by revolving the region bounded by y= -x^2-1 and y=x^2-2x-5 about the line y=11. Question 2: is using the same regions about x=4. The...