Answer:
a) 12989 Ib
b) 2756.3 Ib
Step-by-step explanation:
Density of milk = 64.6 Ib/ft^3
Diameter of tank = 8 ft
radius = 4 ft
a) Calculate force exerted by milk on one end of tank when Tank is full
pressure on strip ≈ 64.6 ( 4 - yi ) i.e. surface of milk = 4
Total force = 129.2 * Â [tex]\int\limits^4_4 {4-y} \sqrt{16-y^2} \, dx[/tex]
∴Force exerted  = 129.2 * Area of semicircle( radius =4 ) * radius
            = 129.2* 8π * 4 ≈  12989 Ib
b) Force exerted when Tank is half full
pressure on strip ≈ 64.6 ( 0 - yi )  i.e. surface of milk = 0
Total force = 129.2 * [tex]\int\limits^0_4 {0-y} \sqrt{16-y^2} \, dx[/tex]
∴ Force exerted ≈ 2756.3 Ib
