A cylindrical tank has a radius of 6.5 ft and an altitude of 15 ft . If a gallon of paint will cover \( 130 \mathrm{ft}^{2} \) 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,
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First, let's calculate the surface area of the cylindrical tank, which includes the lateral surface area and the area of the top and bottom. The lateral surface area is given by \(2\pi rh\), where \(r\) is the radius (6.5 ft) and \(h\) is the height (15 ft). The area of the top and bottom combined is \(2\pi r^2\). Plugging in the numbers, the total surface area comes out to approximately \(2\pi(6.5)(15) + 2\pi(6.5)^2\), which equals around \(500.65 \mathrm{ft}^2\). Since you're applying two coats, the total area to be painted becomes \(500.65 \times 2 = 1001.3 \mathrm{ft}^2\). Now, given that one gallon of paint covers \(130 \mathrm{ft}^2\), you would calculate the amount of paint needed as \(1001.3 / 130 \approx 7.7\) gallons. Since you can't buy a fraction of a gallon, round up to 8 gallons for your painting project!