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We can use the formula r=√S/12.6 to relate a ball’s surface area S (in square inches) to its radius r (in inches). Suppose a ball has a surface area of 415.8 square inches. What is its radius?
Solution
IF the ball is a perfect sphere, the surface area = S = pir^2 = 415.8 and r^2 = 415.8/p
r = square root of 415.8/pi = about 11.5045 inches
If you use a different formula, it’s not a perfect sphere
r=square root of 415.8 divided by 12.6 could mean two different things, depending on whether you intended the square root sign to be over 415.8/12.6 or just over 415.8 and the square root then divided by 12.6
put them both under the square root sign gives square root of 33 = about 5.74 inches
put just the 415.8 under, then r = 20.4/12.6 = about 1.62 inches
But if it’s not a perfect square, then r is a variable, not a constant, so the formula doesn’t make sense