Answer:
Answer: d) -310pi
Step-by-step explanation:
Instantaneous Rate of Change
Is the change in the rate of change of a function at a particular instant. It's the same as the derivative value at a specific point.
The surface area of a cylinder of radius r and height h is:
[tex]A=2\pi r^2+2\pi r h[/tex]
We need to calculate the rate of change of the surface area of the cylinder at a specific moment where:
The radius is r=8 mm
The height is h=3 mm
The radius changes at r'=-9 mm/hr
The height changes at h'=+2 mm/hr
Find the derivative of A with respect to time:
[tex]A'=2\pi (r^2)'+2\pi (r h)'[/tex]
[tex]A'=2\pi 2rr'+2\pi (r' h+rh')[/tex]
Substituting the values:
[tex]A'=2\pi 2(8)(-9)+2\pi ((-9) (3)+(8)(2))[/tex]
Calculating:
[tex]A'=-288\pi +2\pi (-27+16)[/tex]
[tex]A'=-288\pi +2\pi (-11)[/tex]
[tex]A'=-288\pi -22\pi[/tex]
[tex]A'=-310\pi[/tex]
Answer: d) -310pi
