Ormond Oil company wants to paint one of its cylindrical storage tanks. The tank is 50 feet high and has a
circumference of 118 feet. It is resting on the ground, so
only the top and sides of the tank need to be painted. The
paint that will be used costs $18 for each gallon can and
covers 320 square feet of surface area. How much will it
cost to paint the tank? (Remember that the paint can only
be purchased in gallon containers.)

the company must buy 22 gallons to paint this entire area

Step-by-step explanation:

The circumference of the tank is given and is C = 2(pi)r, where r is the area.                                                                              

                                                                                                             118 ft

Here the circumference is C = 2(pi)(r) = 118 ft, which   leads to r = ≈

18.79 ft ≈ r                                                                                                     2(pi)

The area of the sides is A = (circumference)(height), or approximately

(118 ft)(50 ft) = 5900 ft², and the area of the top is A = πr², which here comes to (π)(18.79 ft)² ≈ 1109 ft².  Combining these two sub-areas, we get:

A(total) = 1109 ft² + 5900 ft² ≈ 7009 ft²

To determine how many gallons of paint will be needed to paint only the top and sides, we divide 7009 ft² by the coverage rate, which is

320 ft²

1 gallon

which results in:

7009 ft²

 ≈  21.9 gallons

320 ft² / gallon                          

Since the paint comes only in full gallon cans, the company must buy 22 gallons to paint this entire area.                                                        

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!