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(Solution Library) The surface area of a cone depends on both its height h and radius r. The formula for the surface area (excluding the base of the cone) is A=π

Question: The surface area of a cone depends on both its height \(h\) and radius \(r\). The formula for the surface area (excluding the base of the cone) is

\[A=\pi r \sqrt{r^{2}+h^{2}}\]
  1. Find the function \(A(r)\) that gives surface area as a function of radius only if we know that a cone has a constant height of \(h=\sqrt{44} \mathrm{~cm}\).
  2. Use a differential to estimate the change in the surface area of such a cone if its radius \(r\) decreases from \(r=10 \mathrm{~cm}\) to \(r=9.87 \mathrm{~cm}\).
    Your written work should give the exact value of this differential.
  3. Round your answer to 3 decimal places and enter below.

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Solution: The downloadable solution consists of 1 pages
Deliverable: Word Document


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