Understanding the Rate of Change of Surface Area in an Inflating Spherical Balloon
This video explores the mathematical concepts related to a spherical balloon being inflated. We analyze the rate at which the surface area of the balloon changes with respect to its radius. By applying principles from calculus, we can derive the relationship between the radius of the balloon and the surface area as it expands. Join us to gain insights into how volume and surface area interact during the inflation process and understand the implications for practical applications.
Understanding the Rate of Change of Surface Area in an Inflating Spherical Balloon
E N D
Presentation Transcript
Example: • http://www.youtube.com/watch?v=K7HG0-_WPqk
Ex. Spherical Ballooon • A spherical balloon is being inflated. What is the rate of increase (change) of the surface area with respect to the radius when ?
Ex. Leaky Oil Tank • An oil tank holds 2000 liters of oil, which drains from the bottom of the tank in 30 minutes. The volume of oil remaining in the tank after minutes is At what rate is the oil draining from the tank?
Ex. Rock and Cliff • upwards • Rock experiences gravitational force from the moment it leaves the hand • Since is towards the ground (ie. Opposite direction of motion) velocity begins to reduce immediately • At some time , velocity becomes zero & rock begins to fall back down • From this time () on, acceleration is in the same direction as motion & so velocity increases.
