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Irina-Kira
1 month ago
7

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
Mathematics
1 answer:
PIT_PIT [12.4K]1 month ago
3 0

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.&lt;/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>
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