Rate of change of surface area of sphere
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Chapter 3 - Applications
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Time Rates | Applications
- 01-02 Water flowing into cylindrical tank
- 03 Water flowing into rectangular trough
- 04-05 Water flowing into triangular trough
- 06-07 Ladder slides down the wall
- 08-09 Rate of movement of shadow on the ground
- 10 - A boy on a bike
- 11-12 Two trains; one going to east, and the other is heading north
- 13-14 Water flowing into trapezoidal trough
- 15-16 Movement of shadow from light at eye level
- 17-18 Rate of shadow in the wall of a building
- 19-21 Two cars driving in parallel roads
- 22-24 One car from a city starts north, another car from nearby city starts east
- 25 Two cars that may collide at 12:30 PM
- 26-27 Time Rates: Kite moving horizontally
- 28-29 Time Rates: Two cars driving on roads that intersects at 60 degree
- 30 - Two trains in perpendicular railroad tracks
- 31-32 Train in an elevated track and car in perpendicular road
- 33-34 Time Rates: A car traveling east and airplane traveling north
- 35-36 Time Rates: Lengthening of shadow and movement of its tip in 3D space
- 37-38 How fast a ship leaving from its starting point
- Rate of change of surface area of sphere
- Chapter 4 - Trigonometric and Inverse Trigonometric Functions
- Partial Derivatives
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I believe the answer should
I believe the answer should be negative since the surface area is decreasing
It is not necessary to…
In reply to I believe the answer should by Anonymous (not verified)
It is not necessary to indicate a negative to the rate of change because the problem already said that it is decreasing.
However, the negative is necessary if the problem asks for "How fast is the surface area is changing". For this statement, it is important to determine if the rate of change is decreasing or increasing or perhaps it is an integral part of the problem. The negative sign is necessary for such a case, or an absolute value with word decreasing or increasing will also do.