Engineering Board Exam Reviewer · Related Rates (Time Rates) · hard
A snowball is melting so that its surface area decreases at 1 cm2/min. Find the rate at which the diameter is decreasing when the diameter is 10 cm.
- 1/20π cm/min 0.0159 cm/min
- 1/40π cm/min
- 1/10π cm/min
- 0.0796 cm/min
Answer
A. 1/20π cm/min 0.0159 cm/min
Solution
At d=10, r=5. S=4π r2, so dS/dt=8π rdr/dt. -1=8π(5)dr/dt dr/dt=-1/40π. Since d=2r, dd/dt=-1/20π -0.0159 cm/min.
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