SOLUTION: An error has been made when measuring the internal diameter of a large drain pipe. The measurement is 5% too large. If this measurement is used to calculate the cross sectional are

Algebra ->  Surface-area -> SOLUTION: An error has been made when measuring the internal diameter of a large drain pipe. The measurement is 5% too large. If this measurement is used to calculate the cross sectional are      Log On


   

Question 176597: An error has been made when measuring the internal diameter of a large drain pipe. The measurement is 5% too large. If this measurement is used to calculate the cross sectional area of the pipe calculate
A) the percentage error that will occur compared to the true area
B) the true area of the pipe when the incorrect measured diameter was 796mm. Give your answer in m^2 to 5 s.f


Area=πr^2 or π d^2/4

C) And also solve the problem using the binominal theorem to the degree of accuracy stated.


^2 means squared
Answer by Mathtut(3670) About Me  (Show Source):

You can put this solution on YOUR website!
A)1.05%5E2=1.1025 so error is 1.1025-1=.1025(100)=10.25%
:
B)if the incorrect diameter is 796 mm then the correct diameter is 796/1.05=
758.095mm. incorrect radius=796/2=398 mm or .398 m....correct radius =758.095/2=379.05mm or .379 m
:
incorrect=%28pi%29%28.398%29%5E2=.497+%28m%29%5E2
correct==%28pi%29%28.379%29%5E2=.451+%28m%29%5E2
:
checking error percentage with actual numbers.497-.451=.046:error % is .046/.451=.10197(100)=10.2% error
:
:
C) I will leave binomial theorem to you