Find the cost of lining a topless rectangular tank 4.8 inches long, 12.2 inches wide, and 9 inches deep with zinc, weighing 4.8 pound per square foot, at $2.83 per pound installed
Typo in length ?? (much less than width)
To find the cost of lining the topless rectangular tank with zinc, we need to calculate the surface area of the tank and then multiply it by the weight of zinc.
Step 1: Calculate the surface area of the tank:
The tank has six sides: two ends, two long sides, and two short sides.
Ends:
The ends have dimensions 4.8 inches long and 9 inches deep. The surface area of one end is given by:
Area of one end = length * depth = 4.8 inches * 9 inches = 43.2 square inches
Since there are two ends, the total surface area of the ends is:
Total area of ends = 2 * Area of one end = 2 * 43.2 square inches = 86.4 square inches
Sides:
The sides have dimensions 12.2 inches wide and 9 inches deep. The surface area of one side is given by:
Area of one side = width * depth = 12.2 inches * 9 inches = 109.8 square inches
Since there are four sides (two long sides and two short sides), the total surface area of the sides is:
Total area of sides = 4 * Area of one side = 4 * 109.8 square inches = 439.2 square inches
Total surface area of the tank = Total area of ends + Total area of sides
Total surface area of the tank = 86.4 square inches + 439.2 square inches = 525.6 square inches
Step 2: Convert the surface area to square feet:
One square foot is equal to 144 square inches.
So, the surface area in square feet is given by:
Surface area in square feet = Total surface area of the tank / 144
Surface area in square feet = 525.6 square inches / 144 = 3.65 square feet
Step 3: Calculate the total weight of zinc needed:
The weight of zinc is given as 4.8 pounds per square foot.
So, the total weight of zinc needed is given by:
Total weight of zinc = Surface area in square feet * Weight of zinc per square foot
Total weight of zinc = 3.65 square feet * 4.8 pounds per square foot = 17.52 pounds
Step 4: Calculate the cost of zinc installation:
The cost of zinc is given as $2.83 per pound installed.
So, the cost of installing zinc is given by:
Cost of installing zinc = Total weight of zinc * Cost per pound installed
Cost of installing zinc = 17.52 pounds * $2.83 per pound = $49.66
Therefore, the cost of lining the topless rectangular tank with zinc is $49.66.
To find the cost of lining the tank, we need to calculate the area and weight of the tank, and then multiply it by the cost per pound.
1. Start by calculating the area of the sides of the tank:
- Since the tank is rectangular, it has six sides: the top, bottom, front, back, left, and right.
- The area of each side can be calculated by multiplying the length by the width.
Area of the top and bottom = length * width = 4.8 inches * 12.2 inches
Area of the front and back = length * depth = 4.8 inches * 9 inches
Area of the left and right sides = width * depth = 12.2 inches * 9 inches
2. Convert the area from square inches to square feet:
- Since the weight of zinc is given in pounds per square foot, we need to convert the area into square feet.
- There are 144 square inches in 1 square foot.
Area of the top and bottom (in square feet) = Area of the top and bottom (in square inches) / 144
Area of the front and back (in square feet) = Area of the front and back (in square inches) / 144
Area of the left and right sides (in square feet) = Area of the left and right sides (in square inches) / 144
3. Calculate the total area of the tank:
- To calculate the total area, add the areas of all six sides of the tank.
Total area = 2 * (Area of the top and bottom) + 2 * (Area of the front and back) + 2 * (Area of the left and right sides)
4. Calculate the weight of the tank:
- Multiply the total area by the weight of zinc per square foot.
Weight of the tank = Total area * Weight of zinc per square foot
5. Calculate the cost of lining the tank:
- Multiply the weight of the tank by the cost per pound installed.
Cost of lining the tank = Weight of the tank * Cost per pound installed
6. Substitute the given values and perform the calculations to find the final cost.
Now you can follow these steps to calculate the cost of lining the topless rectangular tank with zinc.
area of base = (4.8)(12.2) inches^2
area of 4 sides = 2(4.8)(9) + 2(12.2)(9) inches^2
add them up, multiply by 4.8 to get the weight in pounds,
then multiply by 2.83 to get the total cost in dollars.