The total cost, we calculate both the volume of the water tank (a cylinder plus a hemisphere) to determine the cost to fulfill it and the surface area of the tank that needs coloring to determine the painting cost.
To calculate the total cost to fulfill the water in the tank and to color the tank, we need to find the volume of the water tank and the surface area of the tank that requires coloring.
Volume of Water Tank
The water tank consists of a cylinder and a hemisphere.
The volume of the cylinder (Vc) is given by the formula πr2h, where r is the radius of the base and h is the height of the cylinder.
The volume of the hemisphere (Vh) is given by the formula ⅓πr3.
Given that the height of the cylinder is 8 m and the diameter of the tank is 6 m (thus the radius r is 3 m), we can calculate the total volume.
Vtotal = Vc + Vh
Vc = π * (3 m)2 * 8 m and Vh = ⅓π * (3 m)3
Once we have the total volume in cubic meters, we can convert it to liters (1 m3 = 1000 liters) and multiply by the cost per liter to find the total cost of water.
Cost of Coloring
To calculate the cost of coloring the tank, we need to calculate its surface area excluding the base of the tank since it is placed on the ground and presumably does not need painting. The surface area consists of the curved surface of the cylinder (2πrh) and the surface of the hemisphere (2πr2).
Adding these two areas together gives us the total surface area that needs to be colored. Multiplying the total surface area by the cost per square meter will give us the total cost for coloring the tank.