How many gallons of paint are needed to cover the inside of a tank with a diameter of 10 ft and a height of 40 ft, assuming 1 gallon covers 100 sq. ft.?

To determine the number of gallons of paint needed to cover the inside of a cylindrical tank, you first need to calculate the surface area that requires painting. For a cylinder, the surface area includes the side area and the area of the top and bottom.

The formula for the lateral (side) surface area of a cylinder is:

[ \text{Lateral Surface Area} = 2\pi rh ]

where ( r ) is the radius and ( h ) is the height of the cylinder. For a tank with a diameter of 10 feet, the radius would be half of that, which is 5 feet. The height of the tank is given as 40 feet.

Now, substituting the values into the formula gives:

[ \text{Lateral Surface Area} = 2\pi(5 \text{ ft})(40 \text{ ft}) = 2\pi(200 \text{ ft}^2) = 400\pi \text{ ft}^2 ]

Next, calculating ( 400\pi ):

[ \approx 400 \times 3.14 = 1256 \text{ ft}^2 ]

Next, you also need to calculate the area