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If a snowball melts so that its surface area decreases at a rate of $ 1cm^2/min, $ find the rate at which the diameter decreases when the diameter is $ 10 cm. $(a) What quantities are given in the problem?(b) What is the unknown?(c) Draw a picture of the situation for any time $ t. $(d) Write an equation that relates the quantities.(e) Finish solving the problem.

a) 1 $\mathrm{cm}^{2} / \mathrm{min}$ and 10 $\mathrm{cm}$b) the rate that the diameter is decreasing when the diameter is 10 $\mathrm{cm}$c) See step for answerd) $\pi \ell^{2}$e) Diameter is decreasing at a rate of $\frac{1}{20 \pi} \approx 0.016 \mathrm{cm} / \mathrm{min}$

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 9

Related Rates

Derivatives

Differentiation

Missouri State University

Oregon State University

Harvey Mudd College

Boston College

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Baylor University

University of Michigan - Ann Arbor

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