A) Circles. Calculate the percentage uncertainty in circular...

A) Circles. Calculate the percentage uncertainty in circular area and the nominal area including uncertainty given: Circle Area = ? r² = ? d² / 4 i) radius is: 12.7 +/- 0.13 cm ii) diameter is: 4.003 +/- 0.0018 inch

Transcript

00:01 Question we want to calculate the percentage uncertainty in a circular area and nominal area including uncertainty given so we want to find percentage uncertainty here we want to find percentage percentage uncertainty when here two areas circular area and nominal area so let's find first for the in the first part of this question we are given here radius so the radius r which is equal to we are given here 12 .7 to minus 0 .13 cm so this is the value of radius r and we are given a circular area so area which is equal to pi r square and the differentiated area with a so we can write d a by a which is equal we can write 2 pi r divided by pi r and d r now we can write d a by a which is equal to 2 multiply by d r by r now we just substitute to value into this formula so you can write d a by a which is equal to we can write 2 multiply by 0 .13 divided by radius value is 12 .7 now we just simplify this equation and we can write here answer is so answer is 0 .0 204 now we just multiply by 100 so d a by a multiply by 100 which is equal to we can write answer is 2 .04 percentage now this is the value is in the percentage or we can say this is relative velocity or this is the relative velocity and when you multiply by 100 this is the percentage uncertainty so this is the percentage uncertainty now for the nominal area so we are given here nominal area and circular area so first we will find for the nominal area uncertainty so area with is equal to pi r square area which is equal to pi r square area which is equal to p multiple value of r is 12 .7 square which is equal we can write here answer is 5 506 .7 centimeter square so this is the value of area and r which is equal to you can write 12 .7 plus or minus we can wear 0 .13 so here we can write value of r and now right right here which is equal to 12 plus 1 plus 13 so we can write 12 .83 centimeter so for that area so we can write pi multiply by value of r is 12 .83 square which is equal to we can write your answer is 570 .1 centimeter square and we want to find the uncertainty so how to find the uncertainty here so we can write uncertainty which is equal to values 517 1 .1 minus we can write 506 .1 which is equal to answer is 10 .4 centimeters square so this is the value of unscertainry we want to find nominal area for that so nominal area which is equal to we can write 506 .7 multiply by if we can…

Question

A) Circles. Calculate the percentage uncertainty in circular area and the nominal area including uncertainty given: Circle Area = ? r² = ? d² / 4 i) radius is: 12.7 +/- 0.13 cm ii) diameter is: 4.003 +/- 0.0018 inch

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