a. A spherical balloon is being filled with air at a constant rate of 2 cm³ per second. Write down the formulae for the volume, V, and surface area, S, of the sphere in terms of the radius, r. dr Use the chain rule for differentiation to find an expression for in terms of r, where t is dt time in seconds. b. Find the rate at which the radius is increasing when the radius is equal to 24 cm. c. The balloon will burst when the radius reaches 100 cm. Find the rate at which the surface area is increasing at that point in time. d. Find the Cartesian equation that relates Vand S. Use appropriate graphing software to plot this function for possible values. Your screenshot should include the side panel that shows your equation and any restrictions on the domain.
a. A spherical balloon is being filled with air at a constant rate of 2 cm³ per second. Write down the formulae for the volume, V, and surface area, S, of the sphere in terms of the radius, r. dr Use the chain rule for differentiation to find an expression for in terms of r, where t is dt time in seconds. b. Find the rate at which the radius is increasing when the radius is equal to 24 cm. c. The balloon will burst when the radius reaches 100 cm. Find the rate at which the surface area is increasing at that point in time. d. Find the Cartesian equation that relates Vand S. Use appropriate graphing software to plot this function for possible values. Your screenshot should include the side panel that shows your equation and any restrictions on the domain.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Part b and d onl
Transcribed Image Text:a. A spherical balloon is being filled with air at a constant rate of 2 cm³ per second. Write down
the formulae for the volume, V, and surface area, S, of the sphere in terms of the radius, r.
Use the chain rule for differentiation to find an expression for in terms of r, where t is
dr
dt
time in seconds.
b. Find the rate at which the radius is increasing when the radius is equal to 24 cm.
c. The balloon will burst when the radius reaches 100 cm. Find the rate at which the surface
area is increasing at that point in time.
d. Find the Cartesian equation that relates Vand S. Use appropriate graphing software to plot
this function for possible values. Your screenshot should include the side panel that shows
your equation and any restrictions on the domain.
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