A milk truck carries milk with density 64.6

Question

A milk truck carries milk with density 64.6 lb/ft^(3) lb/ft³ in a horizontal cylindrical tank with diameter 6 ft.

(a) Find the force exerted by the milk on one end of the tank when the tank is full. (Round your answer to the nearest integer.)

----lb

(b) What if the tank is half full? (Round your answer to one decimal place.) 

----lb

Answer 1

(a) h(x) = 3 - x; a(x) =L(x)dx = (2)(sqrt(9 - x²))dx

F(x) = (w)[integral from -3 to 3] (h(x)a(x))dx

= (64.6)[integral from -3 to 3] (3-x)(2)(sqrt(9 - x²)dx

= 387.6[integral from -3 to 3] (sqrt(9 - x²))dx -

129.2[integral from -3 to 3] (x)sqrt(9 - x^2)dx

= 387.6(9pi/2) = 5480 lb

(b) h(x) = x; a(x) = (2)(sqrt(9 - x^2)dx

F(x) = (64.6)[integral from 0 to 3] (x)(2)(sqrt(9 - x^2)dx

= (129.2)(9) = 1162.8 lb