# A cylindrical paint can has a 6.5 inch inside diameter and is 7.75 inches high. It is being filled with paint at a rate of 120in^3/minute.How fast is the surface area of the inside of the can being coated with paint?I need help plz explain

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Answer:The rate of coating of surface is = 74 inch²/minStep-by-step explanation:diameter = 6.5-inch, height = 7.75-inch, rate of filling or dv/dt = 120 inch/minSince 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 1The volume for the cylinder = V = πr²hdv/dt = πr² x dh/dt, where r is constant120 = π x (3.25)² x dh/dtDh/dt = 120/π x (3.25)²Now differentiate the surface area equation 1ds/dt = 2 x π x r dh/dt + 0 , where r is constantreplace the value of dh/dt in the above equation of ds/dtds/ dt = 2 x π x 3.25 x (120/π x (3.25)²ds/dt = 73.846 ≅ 74inch²/min
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