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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 answer

d) $\pi \ell^{2}$

e) Diameter is decreasing at a rate of $\frac{1}{20 \pi} \approx 0.016 \mathrm{cm} / \mathrm{min}$

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Missouri State University

Campbell University

University of Nottingham

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