Question

suppose radius of earth known to 3595 miles with tolerance of - 0.1 miles what effect does this have on calculation of surface area

Answer 1

The effect of - 0.1 miles tolerance on a 3595 miles radius of earth's surface area calculation is 0.00556 %

SA = 4 π r²

SA = Surface area of a sphere

r = Radius

Actual surface area,

r = 3595 mi

SA = 4 * 3.14 * 3595²

SA = 162325754 mi²

Surface area with tolerance,

r = 3595 - 0.1

r = 3594.9 mi

SA = 4 * 3.14 * 3594.9²

SA = 162316723.5 mi²

% error = ( Actual value - Error value ) / Actual value

% error = ( 162325754 - 162316723.5 ) / 162325754

% error = 9030.5 / 162325754

% error = 5.56 * $10^{-5}$

% error = 0.00556 %

Therefore, the effect of - 0.1 miles tolerance on a 3595 miles radius of earth's surface area calculation is 0.00556 %

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