A cylindrical tank has a radius of $5.5 \mathrm{ft}$ and an altitude of $16 \mathrm{ft}$. If a gallon of paint will cover 140 $\mathrm{ft}^{2}$ of surface, how much paint is needed to put two coats of paint on the entire surface of the tank?
To put two coats of paint on the entire surface of the tank, $\square$ full gallons of paint are needed.
Answer
Since we can't buy a fraction of a gallon of paint, we round up to the nearest whole number. So, we need \(\boxed{11}\) full gallons of paint.
Step 1 ：Given a cylindrical tank with a radius of \(5.5 \mathrm{ft}\) and a height of \(16 \mathrm{ft}\). A gallon of paint will cover \(140 \mathrm{ft}^{2}\) of surface. We need to find out how much paint is needed to put two coats of paint on the entire surface of the tank.
Step 2 ：First, we calculate the surface area of the cylindrical tank. The formula for the surface area of a cylinder is \(2\pi r(r + h)\), where \(r\) is the radius and \(h\) is the height. Substituting the given values, we get \(2\pi \times 5.5 \times (5.5 + 16) = 742.986662573986 \mathrm{ft}^{2}\).
Step 3 ：Since we are applying two coats of paint, we need to double the surface area. So, the total area to be painted is \(2 \times 742.986662573986 = 1485.973325147972 \mathrm{ft}^{2}\).
Step 4 ：Next, we divide the total area to be painted by the area that a gallon of paint can cover to find out how many gallons of paint are needed. So, the gallons of paint needed is \(1485.973325147972 \div 140 = 10.6140958931998\) gallons.
Step 5 ：Since we can't buy a fraction of a gallon of paint, we round up to the nearest whole number. So, we need \(\boxed{11}\) full gallons of paint.
