Calculus 2
posted by Jack .
A circular plate of radius r feet is submerged vertically in a tank of fluid that weighs w pounds per cubic foot. The center of the circle is k(k>r)feet below the surface of the fluid. Show that the fluid force on the surface of the plate is F=wk(πr^2). How to prove this given formula by Evaluating one integral by a geometric formula and the other by observing that the integral is an odd function?
Respond to this Question
Similar Questions

Math  Calculus
Im doing some practice questions and im stumped on this one. The amount of cleaning fluid in a partially filled, spherical tank is given by V = (pi)R(h^2)(pi(h^3))/3 Where R is the radius of the rank, and h is the depth of the center … 
AP calculus
The base of a coneshaped tank is a circle of radius 5 feet, and the vertex of the cone is 12 feet above the base. The tank is being filled at a rate of 3 cubic feet per minute. Find the rate of change of the depth of water in the … 
Calculus
Water is draining at a rate of 2 cubic feet per minute from the bottom of a conically shaped storage tank of overall height 6 feet and radius 2 feet . How fast is the height of water in the tank changing when 8 cubic feet of water … 
Calc
A cylindrical slime tank is placed so that the axis of the cylinder is horizontal. Find the fluid force on a circular end of the tank if the tank is half full, assuming that the diameter is 6 feet and the slime weighs 54 pounds per … 
Calculus
A spherical oil tank with a radius of 10 feet is half full of oil that weighs 60 pounds per cubic foot. Its top is 6 feet underground. How much work is needed to pump the oil out of the tank through a hole in its top? 
Physics/Calculus
A spherical oil tank with a radius of 10 feet is half full of oil that weighs 60 pounds per cubic foot. Its top is 6 feet underground. How much work is needed to pump the oil out of the tank through a hole in its top? 
Calculus
Water is running into an open conical tank at the rate of 9 cubic feet per minute. The tank is standing inverted, and has a height of 10 feet and a base diameter of 10 feet. At what rate is the radius of the water in the tank increasing … 
Calculus
Water is running into an open conical tank at the rate of 9 cubic feet per minute. The tank is standing inverted, and has a height of 10 feet and a base diameter of 10 feet. At what rate is the exposed surface area of the water changing … 
geometry
A hemisphere tank is filled with water and has a diameter of ten feet. If the water weighs 62.4 pounds per cubic foot, what is the total weight of water in a full tank? 
integral calculus
A cylindrical tank of radius 3 ft length 8 ft is laid out horizontally .The tank is half full of oil that weighs 60 pounds per cubic foot. a.)determine the work done in pumping out oil to the top of the tank. b.)determine the work …