anonymous
  • anonymous
As a circular metal griddle is being heated, its diameter changes at a rate of 0.01 cm/min. Find the rate at which the area of one side is changing when the diameter is 30 centimeters.
Mathematics
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anonymous
  • anonymous
As a circular metal griddle is being heated, its diameter changes at a rate of 0.01 cm/min. Find the rate at which the area of one side is changing when the diameter is 30 centimeters.
Mathematics
katieb
  • katieb
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
This is a neat one...okay, so you can automatically put down that the rate of change of the diameter is 0.01 cm/min. The change in the area is dependent on the change in the radius, and hence, the diameter:\[A = \pi*r^2 \rightarrow A = \pi*(d/2)^2 \rightarrow A = \pi*d^2/4\] and taking the derivative,\[dA/dt = \pi*2*d/4 = \pi*d*1/2.\] Plug in the diameter at a given time, and you should get the rate of change at that time.
anonymous
  • anonymous
Sorry, forgot to add -- multiply by the rate of change of the diameter, if I'm not mistaken.

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