Volumes Definition and 182 Threads

Single Var Calculus -- Volumes of Revolution consider the curves y = 6 x = 0 and y = x2+2 Revolve the bound area around the y-axis and find the volume of the product solid. Here's what I did. r = x = (y - 2)1/2 V = pi * INTEGRAL from y = 2 -> y = 6 of r2 dy = y - 2 dy = y2/2 -...

Homework Statement The function V(x) = x(14-2x)(15-x) 0<x<7 models the volume of a box Find the extreme values of V and tell whether these represent the smallest and largest volumes or only the smallest or only the largest volumes Homework Equations The Attempt at a Solution...

1. Let R be the region bounded by the curves y = x2 and y = x + 2. (a) Sketch the region R and label the points of intersection between the two curves. (b) Suppose we rotate R about the x-axis. Compute the volume of the resulting solid. (c) What is the volume of the solid obtained by rotating...

Any reviews of this book? Any would be helpful!

I have to finish this one question that I have come across and I am having a bit of trouble figuring out where to go from what I havee done. The Q is: A copper cylinder is 5.82 +/- 0.06 cm long and has a radius of 2.53 +/- 0.04 cm. Using the appropraite formula, Question Details a) Find...

1. Homework Statement k so here is the equation i need help with that will find me the volume of a sphere 2*pi*y*sqrt(25-(y-1)^2) dy - 5*pi from 0 to 6 the 5 pi is the volume of a cylinder 2. Steps so first i subbed u=y-1 took the 2 pi out of the integral that got me 2 integrals...

This is not a homework question, but a tipsy bar question.The question being: There are two tanks of water, one large and one small, full of water of the same density. You are using engines to rotate one cylinder in each tank, the cylinders being of equal size. Will the cylinder in the larger...

Theres a few key concepts about the disc and washer method that I can't quite grasp and I was hoping if I could get a bit of clarification. 1) How do you find your outer and inner radius? I can provide an example if needed. 2) If a problem has its function, for example f(x)= sec x...

Homework Statement Hi I am trying to find the volume of a shape.I don't need help to solve, but I would like a hand setting these integrals up. I've only recently started doing volumes, so bear with me. Using the curves: y=x x=2-y^2 y=0 Indicate the method used and set the...

Hey guys I am new here i was wondering if anyone can help me understand this problem better Homework Statement The base of a certain solid is the circle x^2 + y^2 = 9. Cross sections of the solid with planes perpendicular to the y-axis are semicircles with their diameter in the base of the...

I have a volume problem that I has been bothering me for a while now, as I have just not been able to figure it out. The question involves finding the volume of the solid generated by revolving the region bounded by y = x, y = 0, and y = 4 around the line x = 6. I tried doing \int ^{4}_{0}16...

Ok, I need some math info and I think this is the right section for my question, but I may be wrong. Is it physics? General math? I don't know. I'd like to know if you can determine the shape of a volume by the rate differences with which it fills up. Let's say you are filling a ball with...

Homework Statement A circle with a radius of (a/2) is bored through the centre of a sphere of radius a. Find the volume of the remaining solid. Homework Equations The Attempt at a Solution I've been trying this for an hour now and I've been trying to find the remaining volume by...

Homework Statement A surface S is formed by rotating a quarter ellipse C about the X-axis. Write an integral that represents the volume enclosed by S. the ellipse is represented by two points, (2,1) at which t= pi/2, and (4,0) at which t=0. Homework Equations Ellipse w/radii a,b, in...

R(x)=x^3 bounded by x=0, x=2 and y=1. a. revolved around x=2 b. revolved around x=10 my pathetic attempt: a. v=pi[(integral from 0 to 1)(2-y^1/3)^2]dy so =pi[4y-3y^(4/3)+(3/5)y^(5/3)]evaluated from 0 to 1 =(8/5)pi b. v=pi[(integral from 0 to 2)(10-x^3)^2]dy I must admit that I...

Homework Statement Find the volume of the solid generated by revolving the triangular region bounded by the lines y= 2x, y= 0 and x= 1 about the line x= 1. Homework Equations V= \int A(x)dx = \int \pi[R(x)]^{2}dx The Attempt at a Solution I used the disk method, in which I found...

This shouldn't be a problem but I just can't this right! Homework Statement Find the volume of the body that is generated when y= 1/x(sqrt(4-x^2)) ,1 <= x <2, is rotated around the y-axisHomework Equations Using cylindrical shells : 2 pi ∫x (g(x)-f(x)) dx The Attempt at a Solution 2 pi ∫x...

A log having the shape of a right circular cylinder of radius a is lying on its side. A wedge is removed from the log by making a vertical cut and another cut at an angle of 45 degrees, both cuts intersecting at the center of the log. Find the volume of the wedge. And as soon as I finish...

Homework Statement A trough in the shape of an isosceles trapezoid is 30 cm wide on the bottom, 80 cm on the top, 50 cm tall, and 10 cm long. It is being filled with water at 0.2 cm3/min. How fast is the water level rising when the water is 30 cm deep. The Attempt at a Solution Well I...

Homework Statement Revolve the region bounded by x=0, x=1, y=0 and y=x^5 about the y-axis use shells to find the volume I know how to set up the integral I just don't know where I'm integrating from. Is it from 0 to 1?

Homework Statement Consider the reaction 2Bi2S3 +9O2 ---------> 2Bi2O3 +6O2 The reaction is carried out and kept at 1.00 atm pressure and 174 C throughout. How many liters of O2 are needed to produce 3.87 L of SO2? How many grams of Bi2S3 are needed? The Attempt at a Solution my...

Homework Statement I'm having issues with this section in calc. I'm not at all sure what I'm doing! Here is the problem I'm having trouble with: Directions: Find the volume of the solids. Problem: The base of the solid is the disk X^2 + Y^2 <= 1. The cross-sections by planes...

Homework Statement Let B be a solid box with length L, width W, and height H. Let S be the set of all points that are a distance at most 1 from some point of B. Express the volume of S in terms of L,W, and H. Homework Equations 4/3(pi)r The Attempt at a Solution I have gotten to...

Homework Statement An ellipse is rotated around the y-axis, find the volume of this solid. Homework Equations x^2 / a^2 + y^2 / b^2 = 1 \pi\int_{a}^-a x^2 dy The Attempt at a Solution I'm having trouble solving this; I know that the upper and lower bounds of the curve occur on...

can anyone give derivations for formulas for finding volume,curved surface areas,total surface areas..of a frustrum...based on similarities of triangles... And anyone belonging to gurudatta coaching centre please add me to skype adikap5735

The volume of a cone = 1 - B H where B is the base of the cone and H is its height. 3 We can think about a cone as the line y = x rotated with respect to the y axis. The...

Homework Statement A solid is definited by the inequalities 0\leqx\leq1, 0\leqy\leq1, and 0\leqz\leqx2+y2. The temperature of the solid is given by the function T=25-3z. Find the average temperature of the solid. The Attempt at a Solution I solved the integral, however I could not...

so i have y = 1/sqroot(3x+2) find volume when rotated around x, regions are x=2 and x=0 equation needed: V= integral Pi*y^2*dx so. i do intergral pi* (1/sqroot(3x+2))^2 * dx so i get pi integral 1/(3x+2) dx so how do i integrate 1/sqroot(3x+2) ? can someone take me...

Homework Statement Houdini is in a giant flask and he stands on a block where his feet are shackled and you need to calculate some vital information to help him out. Cross section of flask = r(h)=10/(sqrt(h+1)) water is being pumped into the flask at 22pi Takes Houdini 10 mins to escape Ignore...

Homework Statement Consider the titration of 20.0mL of a 0.100 M solution of HBrO, a weak acid (Ka=2.5x10-9) with 0.200 M KOH. Calculate the pH of the following volumes of KOH. a. 0.00mL b. 5.00mL c. 10.00mL d. 30.00mL Homework Equations pH=pKa +log [base]/[acid] The Attempt...

In my Cal II, we're discussing finding volumes of revolution using centroids, which we find using moments of x or y. Can someone explain to me what a moment is?

Homework Statement The function is y = 2 - x. The region is bounded by x = 2 and x = 4. Calculate its volume by the shell method by rotating it by the x axis. The Attempt at a Solution This problem has been consuming my mind. I calculated it by the disc method and shell method but I...

Homework Statement http://www.math.rutgers.edu/~greenfie/mill_courses/math152/pdfstuff/w2.pdf problem 2 Homework Equations Work is the integral of force.. The Attempt at a Solution Problem 2: Basically I know how to calculate the work for the cylinder. Since they have...

Volumes: The Disk Method [Resolved] 1. If the area bounded by the parabola y = H - (H/R^{2})x^{2} and the x-axis is revolved about the y-axis, the resulting bullet-shaped solid is a segment of a paraboloid of revolition with height H and radius of base R. Show its volume is half the volume of...

I've encountered a weird problem in my text...somewhat by accident =P My text only covers volumes of revolution through the disk method, and one of the questions was: Find the volume of the solid obtained when the given region is rotated about the x-axis. c) Under y = 1/x from 1 to 4 Using...

Homework Statement Find the volume of the solid obtained by rotating the region under the graph of y=1/x and y=1/x^2 about the vertical axis x=-1 Also given are points on the y-axis (0,2) and (0,5). I guessing these points are specific sections of the graphs where we find the volume...

Ive done this question but from the answers I am getting I can see that I am going wrong, but I don't know where. There are lots of different parts to this question, I will show them all, followed by my attempt at working them out. A Harbour has an average water covered area of approx...

Check please, Volumes for Calculus 1 Been a while since I've done these type of problems, check please! http://img70.imageshack.us/img70/3558/volumes1iy0.jpg" http://img70.imageshack.us/img70/6768/volumes2aa9.jpg" 1. Find the volume of the solid generated by revolving the region about the...

This is an elementary question: restricting ourselves to the euclidean plane, is there a strict definition of what kind of set of points constitutes a region with area? For example, does a set of points describing a circle adjoined with an isolated point outside the circle still constitutes a...

I have a simple question on the set-up of a triangular prism. Strang, Ch. 8: Applications of the Integral pdf page 4 (bottom) and correlates with example 5 on pdf page 5 http://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/8.1-8.3.pdf How is he getting the length of 1-\frac x h

[SOLVED] volumes... last week of calc i was absent when we went over the volume section. y= 1/x, x= 1, x= 2, y= 0,; about the x-axis \int^{1}_{2} \pi \frac{1}{x} dx i don't know what's next. can anyone inform me, please

Homework Statement In spherical polar coordinates, the infinitesimal displacement ds is given by: ds^2 = dr^2 + r^2 d\theta ^2 + r^2 \sin \left( \theta \right)^2 d\phi ^2 Can I find the volume of a sphere using ds? The Attempt at a Solution I know the spherical volume-element is given...

Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y=x^2 y=2x about the x-axis. So i used intergral 0 to 2 (2x-x^2)^2 dx this is wat i got... pi*(((2^5)/5)-(4(2^4)/4)+(4(2^3)/3)) its wrong so wat did i do wrong?:confused:

Homework Statement Assume that the Earth is a sphere with circumference of 24,900 miles. a. Find the volume of the Earth north of latitude 45 degrees. (hint: integrate with respect to y) b. Find the volume of the Earth between the equator and latitude 45Homework Equations circle: x^2 + y^2...

[SOLVED] Volumes of Revolution Homework Statement find the volume of region A in the first quadrant that is inclosed in the parabola 2x(2-x) and the x-axis, of which is rotated around the axis y = -2. Homework Equations y=(4+2x^2) y= -2 piS(from 0 to 2) (R^2 - r^2) The Attempt at...

Consider the given curves to do the following. x = 3 + (y-2)**2, x = 4 Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis. V = ?? **************** I set up the problem like this... V...

I can't find the volume of solid sqrt(x) + sqrt(y) + sqrt(z) = 1. It's a graph but I wish I had a graphing calculator to see it. It's bounded by x=0, y=0, z=0. I'm teaching myself this stuff and think integration using a change of variables by making x=u^2? This would be a transformation of T...

1. find the area common to r=1+cos@ and r=3^(1/2) sin@ 2. find the volume generated by rotating the region bounded by (x-1)^2 + (y-2)^2 = 4 around a. x axis b. y -axis c. x = 3 d. y = 4

hi how can the following be proved using integral methods: a) prove surface area of sphere, radius a, is 4 \pi a^2 b) prove area of a disk, radius a, is \pi a^2 c) prove volume of ball, radius a, is \frac{4}{3} \pi a^3 d) prove volume of axisymmetric cone of height h and base with radius...

Hello Everyone, I am a bit new here, and I hope this will be the correct area to ask for help on this. (I've been away from math for a good number of years). I am trying to figure out how to find the volume of an area removed from a cylinder. Say I have a cylinder with a radius of 6...