a raindrop has a radius of 3 millimeters.If the raindrop takes 6 seconds to evap

Question

a raindrop has a radius of 3 millimeters.If the raindrop takes 6 seconds to evaporate, determine the volume of the raindrop as function of time,assuming that the raindrop is spherical

Explanation / Answer

Solution: Call the volume of the spherical raindrop V and the surface area S. We are told is that the evaporation rate dV /dt is proportional to S. So, there is some constant k > 0 so that dV = -kS dt where we have the minus sign because evaporation amounts to a decrease of the total volume. Next express S in terms of V . For a sphere of radius r, we have 4 3 pr 3 V = S = 4pr2 . and Use the ?rst to express r as a function of V , ( 3V )1/3 r = 4p The di?erential equation becomes , so, dV ˜ = -kV 2/3 dt ( 3V )2/3 S = 4p = 62/3 p 1/3 V 2/3 . 4p ˜ where k = 62/3 p 1/3 k is a new positive constant.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.