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Volume and Surface Area The radius of a spherical balloon is measured as 8 inches, with a possible error of 0.02 inch.(a) Use differentials to approximate the possible propagated error in computing the volume of the sphere.(b) Use differentials to approximate the possible propagated error in computing the surface area of the sphere.(c) Approximate the percent errors in parts (a) and (b).

$\pm 0.005$

Calculus 1 / AB

Chapter 3

Applications of Differentiation

Section 9

Differentials

Limits

Derivatives

Differentiation

Oregon State University

Harvey Mudd College

Baylor University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

06:04

Volume and Surface Area Th…

10:50

The circumference of a sph…

04:38

03:08

Area The measurement of th…

00:44

The edge of a cube was fou…

03:47

01:00

The radius of a circular d…

01:45

09:24

Area The measurements of t…

02:04

For the following exercise…

So you have some. It's you well on way. Measure that their radios, he's, uh, inches inches for radius some it's here or pull that you will. So you want to computer? What is it? Volume. So you all know what's troubling, but there is a the the reduces measure up to, uh, cure asio 0.2 inches. So these, uh, possible here his own error. So some error in then in their radios can be seeing us, uh, build the harder on their will volume. It's so fortunate. Radios More specifically, it's for thirds. Bye. Are cube. So those peace they're in there? It used translate todo there, buddy. Um um, also, it can be approximated by me because all these will be your toe. Both volume with respect there readies terms. Yeah, which is, uh, dealt the heart. So, uh oh, the error volume be approximated like this formula. So it's computer. What is now? So you have that be prime is gonna be If he comes down, he's gonna be out. Bring comes for thirds. Bye. On the power gets our Lord one. Have a good day. Your crime is this, uh so for this particular case, then in the volume can be approximated to be for bye that I'm stayed squirt Yeah, inches square times, huh? DDR which is Shiro Point 02 I just so eso So he gets, uh, four times in 12 disease 64. Oh, for Bye. So these number will be, uh, these D'oh six making multiplied, Dad. Bye 0.0 two. So it's gonna be all these numbers are gonna be also these harder. It's just a squirt. He's gonna be a dangerous thing. Just squared so that the units will be just cute. What's up? Well, you should be so from here, you have that two of these. That's good. Yeah. D'oh One What? They should be goto Bye. 12 then thumbs. So it should be the error. Should be about bye terms. Why, um five point so cute on the wall. Similarly, the same court is there for Syria. He's sir, Is there you? Depends on the radius is equal to 4/3 support for by hard R squared. So these, uh, error in the radios it's gonna be give up on terror. The surface area which can be approximated right differential surface area. So these happens. People too for a video. There you go. Far this surface area. We respect our It's gonna be ableto yes, writing times are it is equal to seems the r Does he look to Delta are Well, we go to ISS Brian. Damn So buildup aren't so well or as being will do that its prime vehicle to So you two come sounds too them's or bye on the power on our gets lowered them's for But are that's you are I'll see how, but they should be. So he right here this is eight aid it That's why I'm saying are 80 square then that that times point or two again? Just cube. So this will be equal to Mmm Oh, he's too. That is 64 about thumbs through. These want eight, but you won't deploy my point. Oh, one. So, uh, these errors is about while I ate just It's good there then right off the Syria. They're well forgot. Device. God damn spy on the air in the service of Mobile Bay volume is gonna do right by them. My point

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