First slide

Rate Measure

Question

A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of when the
thickness of ice is 5 cm than the rate at which the thickness of ice decreases.

Moderate

A

$\frac{5}{90 π} c m / \min$
B

$\frac{90}{5 π} c m / \min$
C

$\frac{9}{5 π} c m / \min$
D

$\frac{90}{π} c m / \min$

Solution

$V = \frac{4}{3} π r^{3}$
$\begin{array}{l} \frac{d V}{d t} = 4 π r^{2} \frac{d r}{d t} \\ 50 = 4 π (15)^{2} \frac{d r}{d t} \\ \frac{d r}{d t} = \frac{50}{900 π} = \frac{5}{90 π} cm / \min \end{array}$

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