1. A spherical balloon is being filled with helium such that its radius is changing at a constant rate of 2 cm/sec. Answer the following, where the volume of a sphere is V = T r3 and the surface area of a sphere is S = 4 r r² . (a) How fast is the volume changing when the radius of the balloon is 10 cm? (b) How fast is the material of the balloon stretching when its diameter is 30 cm?

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter31: Customary Vernier Calipers And Height Gages
Section: Chapter Questions
Problem 16A: The tables for Exercises 15 and 16 give the position of the zero graduation on the vernier scale in...
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Steps:
1) Draw a picture
3) Determine knowns and unknowns
5) Differentiate to relate the rates
2) Assign variables
4) Find an equation that relates the variables
6) Use the known rate(s) to find the
unknown rate
Answer the following, being sure to include units and show all work.
1. A spherical balloon is being filled with helium such that its radius is changing at a constant
rate of 2 cm/sec. Answer the following, where the volume of a sphere is V =T r3 and the
surface area of a sphere is S = 4T1² .
(a) How fast is the volume changing when the radius of the balloon is 10 cm?
(b) How fast is the material of the balloon stretching when its diameter is 30 cm?
Transcribed Image Text:Steps: 1) Draw a picture 3) Determine knowns and unknowns 5) Differentiate to relate the rates 2) Assign variables 4) Find an equation that relates the variables 6) Use the known rate(s) to find the unknown rate Answer the following, being sure to include units and show all work. 1. A spherical balloon is being filled with helium such that its radius is changing at a constant rate of 2 cm/sec. Answer the following, where the volume of a sphere is V =T r3 and the surface area of a sphere is S = 4T1² . (a) How fast is the volume changing when the radius of the balloon is 10 cm? (b) How fast is the material of the balloon stretching when its diameter is 30 cm?
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