Answer:
(a) Approximate the percent error in computing the area of the circle: 4.5%
(b) Estimate the maximum allowable percent error in measuring the circumference if the error in computing the area cannot exceed 3%: 0.6 cm
Step-by-step explanation:
(a)
First we need to calculate the radius from the circumference:
I leave only one decimal as we need to keep significative figures
Now we proceed to calculate the error for the radius:
Again only one decimal because the significative figures
Now that we have the radius, we can calculate the area and the error:
Then we calculate the error:
Now we proceed to calculate the percent error:
(b)
With the previous values and equations, now we set our error in 3%, so we just go back changing the values:
Now we calculate the error for the radius:
Now we proceed with the error for the circumference:
