tolerance-the-radius-r-of-a-circle-is-measured-with-an-error-of-at-most-2-what-is-the-maximum-corres

Question

Tolerance The radius $r$ of a circle is measured with an error of at most 2$\% .$ What is the maximum corresponding percentage error in computing the circles
a. circumference?
b. area?

Sinisa Stura · Accepted Answer

I look the question in hand, The polar Oh, but it&#x27;s We have a circle with radius R. Um, so that we make and they&#x27;re in the mission of our That would be by our plus the are, in which case, we would have Okay, certain with slightly great conference around the area flu. What were given use the percentage error over the mission. The error in miserable with French. Oh, you&#x27;re Are you hear a point? Oh, too. The questions for a for B. What is the maximum corresponding percentage error in computing? The circumference of the conference is to but, um, the air. Yeah, by we&#x27;re So what happens with the sea of things on the A over a If this is the case for equal to their pointed to within. So the air is within a point. Let&#x27;s assume that we&#x27;re making a there for so we can work with the absent. That would be they think you in the room in regards to at a certain are here. Here. Uh, time the, uh, the river off to part costal with the virus. Two parts. Uh, D c Ever see over cancel for the percentage error. All the differential. The percentage of the air off measurable off the conference is the same as percent. Oh, the radio said the sea by sea with Is there a point to riches? So, during the Christians, what is the mixing? Of course. Polling, percentage error and computing circles Go, Prince Mexico. Cool, uh, foot around the area. The hey, by the way, you and by the time to find two so no d a people to find the on the a r a. You are divided by quit. Cancel, cancel. Cancel With one of the stand here to the, uh, over they are for this you no clue. What&#x27;s the story with time? 4%. 4% to answer the question. What is the Mexico corresponding percentage Error in computing area Maximum for here? I hope so.

Robert Daugherty · Answer

section 3.9 Problem number 45. So, in this case, they&#x27;re telling us that the radius of a circle so the radius is measured, um, with it most an era of 2% and were asked to figure out what is the corresponding error in the computation of a the circumference and b the area. Okay, so what&#x27;s the formula for the circumference of a circle? So the circumference of a circle is two pi r. So if we know that our has an air message of 2% that I know that there is a 2% error four the circumference. So it&#x27;s on the same order of magnitude as the radius. And then what is the area of the circle? The area is equal to pi r squared. So what this tells me is that if I&#x27;ve got it most a 2% area, 2% error message, error, tolerance in the radius. Then it&#x27;s gonna be order of that squared. So it tells me that I&#x27;m going to have 4% error. It&#x27;s for the area calculation. So it&#x27;s on the order of magnitude of r squared

Sajin Shajee · Answer

you be simply training company The Changing Airfields conference so little first to seize he could Are these these two pi r k c during c b o t r. Five that&#x27;ll be This is supposed to be resting. Shira 0.2 dc divided by sees your 0.2 What is the answer? A pie? Ours. Where? T k two by r e R E a a two teams e r prettify Are we just list I ve quoted tweet you, you you e school?

Amrita Bhasin · Answer

Okay. The driven of six X squared is 12 ax. Therefore, we know the maximum error 12 times, 30 times 0.1 gives us 36 centimeters squared. Therefore, relative errors. The area over the surface area therefore 36 divided by six times 30 squared gives 0.0 6/7 on then this ring as a percentage times 100 would be 0.67% for part B. We know that if us his pyre square that s prime of our In other words, the derivative would be two pi r. Therefore, we have to pie times 24 times changing our gives 9.6 pie centimeters squared.

Jack Chen · Answer

in this programme. We No way. We are given her, um, disco with radius and the room to find out the maximum era for the area. So for this, the area is given by Para Square. So I think not veto lower case out to be the Radius and the captor. I took the area in a different show because to two pi r yeah. So the mix era is just the A And we already know what&#x27;s a radius and the words like PR, which is even in the program. So we can just directly Prague in those values. So a nano have 9 26 pie. Don&#x27;t forget we have a unit and the relative era is given by D A over a and the word in out of the air in a So just probably in those functions in the some consolation and, you know, have twice of PR over in the beginning project beyond Dara. So we have, um, two times 0.2, divided by 24 seats around 0.17 and the present age Kara for this area, we just cameras this previous results to be a a president, remember, which is 1.7%

Sinisa Stura · Answer

Hello. Problem about the measure of a que You only five off Cuba on the called the remaking Their initial by for the the new coupe for alarms. Blood on the fun, huh? Way that place spring. So how about how much would what happens when you do you? What happens with the surface area on what happened, won&#x27;t you? You? Yeah, over the It&#x27;ll cute. Measured within a year at most. Is there a 0.5 degrees between the divided by the actual five? Absolutely. Your 0.5. What happens to the surface area? Well, the third area for cube in regards to you six faces of it&#x27;s great group on the question. The with this With what? Let&#x27;s find two years differential. The room that said this is Mitchell Eggs era the river off. If can we go? Thanks. Equals a zero time. What? You that would find What? The derivative off you. Yeah, Think All right. All two x squared, like throw Prove it. But French, the air you will make measuring surface area. Given that we make your measuring the ratio off the you over. Go where we can cool one hit. We can&#x27;t this risk here. Two fine. The such that it&#x27;s within 5% off the actual measuring. So the surface area will be within two times 10%. No, we have Rick congressional correctly 0.5, because cover 0.5%. Two times zero point. You want percent, huh? The volume? I never looked at the volume of the Cube for three on. We want to see what happens with differential in the ratio to the morning itself. Very fine TV to be the river off the hopefully right. What is a derivative of X to the power? 33 three. We&#x27;re ratio Davey for you three divided by three. We can for two. Three of one is we have three times. Well, again, Florence percent with one point. So to answer the question, what is the maximum corresponding percentage? Air in computing Keep surface. Uh, volume one point far. There we have. That is the the problem. I hope it helps

Problem

Tolerance The edge $x$ of a cube is measured with…

Problem 45 Easy Difficulty

Tolerance The radius $r$ of a circle is measured with an error of at most 2$\% .$ What is the maximum corresponding percentage error in computing the circles
a. circumference?
b. area?

Answer

A. 2$\%$
B. 4$\%$

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George B. Thomas, Jr. Maurice D. Weir, Joel Hass

Thomas Calculus

Grace H.

Anna Marie V.

Kayleah T.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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A. 2$\%$B. 4$\%$

Thomas Calculus

Grace H.

Anna Marie V.

Kayleah T.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

George B. Thomas, Jr. Maurice D. Weir, Joel HassThomas Calculus

Grace H.

Anna Marie V.

Kayleah T.

Michael J.

A. 2$\%$
B. 4$\%$

George B. Thomas, Jr. Maurice D. Weir, Joel Hass

Thomas Calculus