Calculus II
posted by RuggedChild .
A coneshaped water reservoir is 20 ft. in diameter and 20 ft. deep. If the reservoir is filled to a depth of 10ft., then write the integral which represents the amount of work required to pump all the water to the TOP of the reservoir.

The work required is proportional to the height, measured from the bottom.
This integral is S (pi*R(H)^2)*(density)*g H dH. S denotes the integral sign
The cone radius as a function of height is R(H) = H/2
Integrate from H = 0 to h = 20 ft
In these British units, (density* g = 62.4 lb/ft^3. The answer will be in ftlb
Respond to this Question
Similar Questions

math
There is a water reservoir beneath a circular garden to supply a fountain in the garden. The reservoir has a 26inch diameter. The garden has a 12foot diameter. How much of the garden doesn't contain the water reservoir? 
math
there is a water reservoir beneath a circular garden to supply a foutain in the garden.the reservoir has a 26inch diameter.the garden has a 12foot diameter. how much of the garden does not contain the waer reservoir? 
calculus
1. A conical reservoir has a depth of 24 feet and a circular top of radius 12 feet. It is being filled so that the depth of water is increasing at a constant rate of 4 feet per hour. Determine the rate in cubic feet per hour at which … 
physics
Heat Q flows spontaneously from a reservoir at 481 K into a reservoir at 298 K. Because of the spontaneous flow, 2760 J of energy is rendered unavailable for work when a Carnot engine operates between the reservoir at 298 K and a reservoir … 
phys
Heat Q flows spontaneously from a reservoir at 481 K into a reservoir at 298 K. Because of the spontaneous flow, 2760 J of energy is rendered unavailable for work when a Carnot engine operates between the reservoir at 298 K and a reservoir … 
calculus
A reservoir is in the form og the frustum of a cone with upper base of radius 8ft and lower base radius of 4 ft and altitude of 10ft. The water in the reservoir is xft deep. If the level of the water is increasing at 4ft/min., how … 
physics I
A spherical reservoir that contains 4.55 105 kg of water when full. (h = 7.70 m.) The reservoir is vented to the atmosphere at the top. For a full reservoir, find the gauge pressure that the water has at the faucet in each house. Ignore … 
math
water flows into a reservoir at 2000l/min. the depth of the reservoir is to be kept constant by installing some discharge pipes 1m below the surface of water in the reservoir and diameter of the pipes are 25mm. calculate the number … 
Physics
The popular Super Soaker water guns are powered by compressed air (provided by a hand pump used by the operator.) A certain model has a cylindrical reservoir (where the water is held) 8.00 cm in diameter and a barrel (where the water … 
Differential calculus
reservoir has the shape of a rightcircular cone. The altitude is 10 feet, and the radius of the base is 4 ft. Water is poured into the reservoir at a constant rate of 5 cubic feet per minute. How fast is the water level rising when …