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Solve the given problems by finding the appropriate differential.If the diameter equals the height, what is the volume of the plastic that forms a closed cylindrical container for which the radius is$18.0 \mathrm{cm}$ and the thickness is $2.00 \mathrm{mm} ?$

Calculus 1 / AB

Chapter 24

Applications of the Derivative

Section 8

Differentials and Linear Approximations

Derivatives

Baylor University

University of Michigan - Ann Arbor

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:05

Use the differential formu…

02:04

Solve each problem.Vol…

09:41

Solve by setting up and so…

02:46

Solve each problem.Wil…

00:52

Write a differential formu…

01:12

01:04

01:00

01:24

02:43

Solve each problem.Sto…

So for this problem, we know that we are given a cylindrical tank with a diameter five meters in the height of 20 meters. And we want to know what the error in our volume would be. Something that we're going to need your or volume formula, which is going to be equal to pi r squared H. And in order to find our error that occurs from impart a height of 20.1, we're going to take the derivative of this equation for volume. With respect to H. That means that DVD is just going to be equal to pi r squared d h. And from here we know that our radius, which is half of our diameter, is just going to be 2.5 meters. Um, so we play that in 2.5 squared and D H is the difference in our age. Value from are given said 20.1 minus 20 is going to be 0.1. So when we saw our error in our volume here is going to be equal to about 1.963 cubic meters and for part B were essentially doing the same thing. The only difference is we're told that our diameter now is going to be five foot one meters in our height will be 20 meters. I'm so again we're going to use the volume formula. So our volume is equal to pi r squared H. But this time since we want to know what the change in the diameter, what would affect the change in the diameter will have That means that we're going to you want to take the derivative with respect to our So when we do that, we get Devi is equal to two pi r h d r And so our change in radius is going to be ah half of this change in our diameter So d R is going to be a 0.5 our radius. We know original SUV 2.5 high is 20 a n d. R is 0.5 so I mean we'll find this out. Our error in our volume in this case is going to be about 15.708 cubic meters

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