Answer:
The rate of coating of surface is = 74 inch²/min
Explanation:
diameter = 6.5-inch, height = 7.75-inch, rate of filling or dv/dt = 120 inch/min
Since the differential of an equation is basically its rate of change with respect to another variable.
Radius = d/2 = 6.5/2 = 3.25 inch, ds/dt = ? can also be understood as the rate at which the surface area of the cylindrical paint can is coated.
We know that the surface area of a cylinder = 2πrh + 2πr², this is equation 1
The volume for the cylinder = V = πr²h
dv/dt = πr² x dh/dt, where r is constant
120 = π x (3.25)² x dh/dt
Dh/dt = 120/π x (3.25)²
Now differentiate the surface area equation 1
ds/dt = 2 x π x r dh/dt + 0 , where r is constant
replace the value of dh/dt in the above equation of ds/dt
ds/ dt = 2 x π x 3.25 x (120/π x (3.25)²
ds/dt = 73.846 ≅ 74inch²/min