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$$ \begin{array}{l}{\text { (III) What, roughly, is the percent uncertainty in the volume }} \\ {\text { of a spherical beach ball whose radius is } r=0.84 \pm 0.04 \mathrm{m} \text { ? }}\end{array} $$

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Physics 101 Mechanics

Chapter 1

Introduction, Measurement, Estimating

Physics Basics

Rutgers, The State University of New Jersey

University of Washington

Simon Fraser University

McMaster University

Lectures

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

09:56

In mathematics, algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.

0:00

(III) What, roughly, is th…

02:52

01:59

What, roughly, is the perc…

01:57

The radius of a spherical …

01:33

If the radius of a sphere …

02:36

49. The radius of a spheri…

01:46

In continuation of the pre…

00:59

(II) What is the percent u…

00:40

00:33

What is the percent uncert…

00:44

(II) What, approximately, …

our question, states, Um what roughly is the percent uncertainty in the volume of a spirit? Kal Beach Ball, Who's radius is our equal? 0.84 plus or minus 0.4 meters. So's our I'm sorry, 0.4 meters. So the 0.4 meters is our uncertainty on our radius. The question then is what is the percent uncertainty where percent uncertain here, right as per cent, Delta V. In order to do this, we first need to calculate the volume of the of the spherical beach ball. In order to do that, we're going to use the volume of a sphere which is 4/3 pi r to the third. Where are here is just going to be the 0.8 form meters, Not including the uncertainty. So 4/3 pi R to the third playing in the 0.4 meters. Oh, it's all gonna be cute. If you carry out this calculation, you get 2.483 cubic meters. Oh, now we want to find the thief uncertainty of our volume or Delta V. In order to do this, we need to find first the upper and lower volume bounds that we could have with the uncertainty were given for our radius. So to find the upper one will calculate the volume What we'll call the Max using the maximum amount of radius that we could have with our uncertainty. So that would be 0.84 plus 0.4 which is zero a date. So we're gonna have 4/3. Hi, our max cubed. Where are Max is equal to 0.8. So I'll go ahead and click that in here. 0.8 and then that's gonna be Cube. This comes out to be 2.145 cubic meters. I'm sorry not to 0.1452 point 855 cubic meters. Okay, Now we need to find the minimum volume that we could have. Or when I'll call the men again, we're gonna have the same equation for volume 4/3 pi r cubed. But now rr is our men. So 4/3 pi our men. Now we get our men by taking zero pointing for and then subtracting our uncertainty of 0.4 So that gives us for third times pi kind 0.8. Nice meters. Cute. This comes out to be 2.145 cubic meters. Okay, so now to get our uncertainty, Delta V. We need to find the difference between our maximum and minimum volume values and then divide that by two. So Delta V is equal to 1/2 the max. It's attracted the neck. Carry out this calculation. This comes out to be 0.355 cubic meters. 0.3 surprise fine cubic meters. Okay. But the question doesn't ask for the uncertainty in our volume. It asked for the percent uncertainty and volume relative to the calculated volume of the sphere. You know, to do that, we use our formula for percent uncertainty which is going to be equal to the ratio of the uncertainty. Delta v divided by the volume and then we need to multiply that by 100% to convert that into a percentage. Now if we go ahead and plug in arc, up are calculated Delta V, which is 0.355 cubic meters, and we divide that by the which we found to be two point for a three cubic meters. We multiply all of that by 100% we get 14 0.3 percent, which is just approximately 14% which could go ahead and boxing as our solution.

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