The entire surface of a free-standing cylindrical tank with an exposed flat bottom must be painted. What is the total surface area to be painted if the tank is 45 inches in diameter and 18 ft high?

To determine the total surface area that must be painted on a free-standing cylindrical tank with an exposed flat bottom, you need to consider both the lateral surface area of the cylinder and the area of the bottom.

1. Calculate the lateral surface area of the cylinder:

The lateral surface area (A_lateral) of a cylinder is given by the formula:

[

A_{lateral} = 2\pi rh

]

Where:

• r is the radius of the cylinder

• h is the height of the cylinder

First, we need to find the radius of the tank. The diameter is 45 inches, so the radius (r) is:

[

r = \frac{diameter}{2} = \frac{45}{2} = 22.5 \text{ inches}

]

To use this value in calculations, convert it to feet, since the height is given in feet:

[

r = \frac{22.5}{12} = 1.875 \text{ feet}

]

The height (h) of the tank is given as 18 feet. Plugging the values into the formula