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anonymous

  • 5 years ago

a) Find the average rate of change of the area of a circle with respect to its radius r as r changes from 4 to each of the following. (i) 4 to 5 _______ (ii) 4 to 4.5 _______ (iii) 4 to 4.1 _______ (b) Find the instantaneous rate of change when r = 4. A'(4) = ______

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  1. anonymous
    • 5 years ago
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    Formula for area: \[A = \pi r^2\] To find average rate of change, find the value of A at both radii and find the difference. i.) \[A _{1}=\pi (4)^2 = 16\pi\] \[A _{2}=\pi (5)^2 = 25\pi\] \[\Delta A = A _2 - A _1 = 25\pi - 16\pi = 9\pi\] I'll leave ii. and iii. for you to do. For part b - Find dA/dr and let r = 4. \[A = \pi r^2\] \[dA/dr = 2\pi r\] \[dA/dr (4) = 2\pi (4) = 8\pi\]

  2. anonymous
    • 5 years ago
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    Oh, whoops. For the average rate of change, you have to divide the change in area by the change in the radius. The first one is (25pi - 16pi) / (5 - 4) = 9pi / 1 = 9pi. This doesn't change the answer for the first one, but you have to remember that for the other two.

  3. anonymous
    • 5 years ago
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    thanks , I got it.

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