Answer:
The rate of surface coating is = 74 inch²/min
Step-by-step explanation:
The cylinder has a diameter of 6.5 inches and a height of 7.75 inches, with a filling rate or dv/dt of 120 inch/min.
<pthe differential="" of="" an="" equation="" represents="" the="" rate="" change="" in="" relation="" to="" another="" variable.=""><pradius d="" inches="" ds="" can="" also="" be="" viewed="" as="" the="" rate="" at="" which="" interior="" surface="" area="" of="" paint="" is="" being="" coated.=""><pthe formula="" for="" the="" surface="" area="" of="" a="" cylinder="" is="" given="" by="" which="" represented="" as="" equation=""><pthe formula="" for="" volume="" the="" cylinder="" is="" v="πr²h.</p">
dv/dt = πr² x dh/dt, where r remains constant.
120 = π x (3.25)² x dh/dt.
Now, dh/dt = 120/π x (3.25)².
Next, differentiate equation 1 for the surface area.
ds/dt = 2 x π x r dh/dt + 0, where r remains constant.
Substituting the value of dh/dt in the ds/dt equation yields:
ds/dt = 2 x π x 3.25 x (120/π x (3.25)²).
Thus, ds/dt = 73.846 ≅ 74 inch²/min.
</pthe></pthe></pradius></pthe>
