Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Show that the centroid of the solid semiellipsoid of revolution $\left(r^{2} / a^{2}\right)+\left(z^{2} / h^{2}\right) \leq 1, z \geq 0$ lies on the $z$ -axis three-eighths of the way from the base to the top. The special case $h=a$ gives a solid hemisphere. Thus, the centroid of a solid hemisphere lies on the axis of symmetry threeeighths of the way from the base to the top.

$\frac{3}{8} h$

Calculus 3

Chapter 15

Multiple Integrals

Section 7

Triple Integrals in Cylindrical and Spherical Coordinates

Missouri State University

Oregon State University

Harvey Mudd College

Idaho State University

Lectures

04:18

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data. Integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. The area above the x-axis adds to the total.

26:18

In mathematics, a double integral is an integral where the integrand is a function of two variables, and the integral is taken over some region in the Euclidean plane.

15:20

Centroid of solid semielli…

06:58

Centroid of a solid semiel…

01:08

Find the centroid of the s…

any side from bloodies. Uh, it's symmetric with respect rules. They well fear we have our base were in use a here. Ah, this is the stones. Here is a That's a circle on the height here is inch You have these shape Now that we're when we can see the ring deal per part. So far See bigger dogs. Zero. So you have that hide there Each have thus these volume I want to find the century on. So it is described by the questions that C is veered honorable zero and then are over and you squared plus C over age squirt is in less than one see on to find the I want to find this the century for this vision. Really san trying since trunk. So, um since it is symmetric about that angle there, you know, ceiling to go Corneas. Ferre. So the is this nose they're here. Is this incredible circles? It's gonna lie along the Z axis so the centrally will have co ordinates zero zero some height She not where we see not is equal to the average value for C and that can be computed as one over the volume of that region that was in trouble during over the valuable Foresee E x. Why? Easy to We're gonna have the diary. Cylindrical coordinates. See? Cylindrical. Um, so here, insulin trickles. We would have that. We'll see. Since I see spotty, she's gonna be given by these. You have their age from here. You have a We have here Z from our so that disease occur. Um, r squared are over a squared plus, See, over age square. Is he called the one So that, uh, the bound foresee will be that sees between zero on, uh, the Pacific solution for about thirties? I wouldn't doubt. Over there, we have c squared over each square school one minus r squared over r a square. Sort of see will be on a particular school wanted by my age. So be age Stance square The one miners are square over a squared, so that would be there over bound for Z one square. The one minus r squared over a squared. I'm Dana was we can not this year or are was from to what away are from zero up to a from our angle federal So there were grounds for theater, so that they don't go from Syria due to buy so that these volumes Well, you know, the we equal to Did you go from zero to buy these and then from zero up to a You are then for C. C. Goes because you know, here on the he's found here on the double B age times square root of one miners are square or a squared being the bullet Mullinix are so that doing this interview to integrate first easy respect to see that is just going to see but which it between each has his curdled one minus are square eight square is your vehicle tool page Ramses Square would one minus R squared over eight square. Great. So you know dot minus zero? I think so. We would have on the b c drove turning to age times are square root one minus r squared over a squared. You are in the theater. I was from zero up to a kid from zero up to two. Why? So for these universal, we could make a new substitution. We let this thing thinking that circle square toe you to vehicle to one minus are squared or a square then how it is you do You will be able to minus two are or minus large er over a squared. So that that will we have Here they are. We are sort of rdr It's gonna be moving down Governors of minus a squared do you over to so that these usual well, the angel of ah, miners, they squared. Um what man sees? Quote, uh, to and then square root? Well, if you they have a you. So now for the bones for what is your day on what issue? Uh, zoo to your to a more people toe one might say squared over a squared. Are you single? The one minus one? That issue I'm you have zero people do one So that the Cinderella B minus a the square house on them have control. You did a one heart, Which is you did it. Three hubs tends to hurts. So these were comes off of you minus a squared thirds You 30 three halfs from these about a week between you're on one seal done warm will be going to minors. He squared thirds. Oh, them 03 house minus, uh, one So that these of people to, um mine is mine. Isso e squared shirts undying. Ah, well, we're gonna get not from there so that eat squid shirts to love each stems e squared thirds, and then we have be seen to the left from zero up to buy. Well, be fair. Um, which is gonna be able to to buy took duck comes to buy some things will be the volume. No, we won't back regiones able to these to buy Sam's age Times a a squared third's is the volume. No, um, you have to complete this interval. So for died angel. See? Are you see? Okay. Our defense on da all the bounds should be the same is the same region Ah, see goes from zero up to each times the square root of one minus r squared over a squared That is it tough? I'm being I rose from zero up three. There are those from Syria off the do pie eso Well, doing these drills being drill. We'll see. You see, I need to have these people to, uh c squared hums. So these evaluated at that point at our age, their squid of armor this r squared over a squared zero people too h squared on these That a square makes the square go ways of the baby The park square and bean pops. Well, I'm no zero. So we're gonna have these udrew, um, to these part is gonna be, ah, so that quarantine beats we get a I'm each square halves h squared. House was integral from zero by angel from zero off bouquet. Ah. Oh, are times he's one minus are squared over. He squared. Um, the are he fear I was So now here. Well, you have the drove Our mine is a drill of our cube where it squared. So these with the the journal of these, with respect, war is gonna be our squared hubs minus our to fourth. Invited by four. Mm. That about four times a squared. So it would be evaluating damaging a zero, which will leave us B squared hubs minus eight to the fourth power. I read it by four. EMC squared on that minus. You said all these councils. That's how you get on the square and complex for that. Squared to be a squared times 1/2 minus one for on, uh, for 1/2 is equal to 2/4 number. There's well, so we have two minus one for so 14 two people to a squared before. Yeah, Dad, been Well, that's gonna be the scene to go. That would be H squared house. Thanks. Done. Hey, squared more damn! 00 have to By Onda. Uh, well, this is drugs to buy to buy so that the whole thing would be h squared humps I m c square, um, over four comes to pie. So, uh, to to a vehicle to r h squared or eight squared by Former four. So Well is not in journal about it. Really? The central here is that value below that he's the this part, so things seem not to If I done see not the reasonable to the average value. Percy the sea coordinate 40 centres Waas Who were these is value. Is that why you squirt? I'm saying scored. I'm spy over for divided by the volume that is equal to not so to by simple toe by age eight squared over how me to buy So these people to finally do these These were not I said, you know people dio mayci square Times Square times by them's three Fuller, Not there. Is that so? There were four times to by James. I'm so, um, hands each times a squirt. So that square councils these councils, by way. So that is gonna be each times age three. Yeah, but we have for yeah, students already. Age 343 eights. That is gonna be the height, height of this century to each ems threes.

View More Answers From This Book

Find Another Textbook

06:27

Determine the equations of the tangent lines from the point (a) (1,10) (b) (…

03:25

Find the equations of the lines and plot the lines from Exercise $53$.

02:17

In 1990 the Massachusetts Non-Resident State Income Tax calls for a tax of $…

04:45

Determine the derivative at the given point on the curve using equation (2).…

03:36

Use the first derivative to determine where the given function is increasing…

02:38

$f(x)=\{\begin{array}{c}9 x+5 \text { if } x \geq 1 \\ x^{2}+7 x+6 \text { i…

01:09

You are given a pair of equations, one representing a supply curve and the o…

03:05

The following $(x, y)$ pairs give the advertising dollars (in millions) spen…

02:40

(a) Find the $x$ -intercept(s); (b) Find the vertical asymptotes; (c) Find t…

01:59

Short segments of the tangent lines are given at various points along a curv…