The circumference of a sphere was measured to be 82.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area._________
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You need to remember the formula of the circumference of circle, hence you need to use this formula to find the radius of sphere such that:
`C= 2pi*r =gt r = C/(2pi)`
You need to evaluate the surface area of sphere such that:
`A = 4pi*r^2`
Substituting `C/(2pi)` for r yields:
`A = 4pi*C^2/(4pi^2)`
Reducing like terms yields:
`A = (C^2)/pi`
You need to remember that linear approximation means to use the tangent line to the given function at a point to find the approximate value of the function around that point.
Hence, you need to differentiate both sides the formula of area such that:
`dA = ((2C)/pi) dC`
Substituting 82.000 for C and 0.5 for dC yields:
`dA = (164.000/pi)*0.5`
`dA = 26101.410 `
Hence, evaluating the maximum error in the calculated surface area yields 26101.410.
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