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Sample Problem 1.01 Estimating order of magnitude, ball of string The worlds largest ball of string is about 2 m in radius. Toballs builder most unhappy. Instead, because we want only the nearest order of magnitude, what is the total length L the nearest order of magnit ude, we can estimate any quanti of the string in the ball? ties required in the calculation. KEY IDEA Calculations: Let us assume the ball is spherical with radius R-2 m. The string in the ball is not closely packed (there are uncounta ble gaps between adjacent sections of string) To allow for these gaps, let us somewhat overestimate We could, of course, take the ball apart and measure the to- tal length L, but that would take great effort and make the

5. First, work on Sample Problem 1.01 Estimating order of magnitude, ball of string, page 4 in H&R,W, to estimate the length of string of the ball. In this Sample problem, the shape of the cross section of the string is assumed to be a square and ¾ns 4 was used to simplify the calculation. Solve this problem again, assuming the shape of the cross section is a circle with a diameter of 4 mm, and without the simplification. (You may still be able to solve it without a calculator.) What is the order of magnitude in your answer. (6 points)

Can someone help explain what magnitude is and how to work out the problem and get the correct answer?

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