an open rectagular box with length of 6 feet, width of 4 feet and height of 2.5 feet is to be painted on all exterior sides, including the bottom,

with a special waterproof coating. Each gallon of this special coating covers 12 square feet of surface area and costs $36.00. The box
is then to be filled with water that weighs approximately 62 pounds per cubic foot.

If I were filling it with water, I would use the waterproof paint on the inside I think :)

area of bottom = 4*6 = 24 ft^2

area of ends = 2 * 4 * 2.5 =20 ft^2

area of sides = 2 * 6 * 2.5 = 30 ft^2

total area of exterior (no top on it) = 74 ft^2

cost of paint = (36/12)*74 = $222 if you can buy a part of a gallon but if the store only sells whole gallons then we need
74/12 = 6.16 gallons
so we must buy 7 gallons
cost = 7 * 36 = $252
and we use the rest of the can to paint the roof of our truck.

the volume of the box is 6*4*2.5 = 60 ft^2 which at 62 pounds per gallon (fresh water, don't see much of that, ours weighs 64) = 3,720 pounds of ater

To calculate the surface area of the box, we need to find the areas of each side and then add them together.

The front and back sides of the box have the same dimensions, so the area of each is length multiplied by height, which is 6 feet x 2.5 feet = 15 square feet.

The two side walls also have the same dimensions, so the area of each is width multiplied by height, which is 4 feet x 2.5 feet = 10 square feet.

The bottom of the box has the dimensions of length multiplied by width, which is 6 feet x 4 feet = 24 square feet.

We also need to consider the top of the box, which has the same dimensions as the bottom, so its area is also 24 square feet.

Adding up all the sides, we have 15 + 15 + 10 + 10 + 24 + 24 = 98 square feet.

Now, let's calculate how many gallons of the special waterproof coating we need. Each gallon covers 12 square feet, so we divide the total surface area of 98 square feet by 12:

98 square feet / 12 square feet per gallon = 8.1667 gallons

Since we cannot purchase a fraction of a gallon, we need to round up to the nearest whole gallon. Therefore, we will need to purchase 9 gallons of the special waterproof coating.

If each gallon of coating costs $36.00, then the total cost for coating the box will be:

9 gallons * $36.00 per gallon = $324.00

Now let's calculate the weight of the water that will fill the box. The volume of the box is found by multiplying its length, width, and height:

Volume = 6 feet * 4 feet * 2.5 feet = 60 cubic feet

Since water weighs approximately 62 pounds per cubic foot, we can calculate the weight of the water in the box:

Weight = Volume * Weight per cubic foot = 60 cubic feet * 62 pounds per cubic foot = 3720 pounds.

Therefore, the box, when filled with water, will weigh approximately 3720 pounds.