A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 for g and 3.14 for . Round your answer to three significant digits.) W=_________
To set up this problem, I tried by taking the area of one slice of water to be pi r^2. Then multiply this by 1000 kg/m^3 to get the volume of one slice.
Now I want R as a function of, lets say y. We know the area of a circle is r^2+y^2=3^2. So r=sqrt(9-y^2). Also, the distance for any slice from the top is 7-y.
After this I tried integrating from zero to six of the function 1000*pi*(9-y^2)*(7-y). This came out to be 36000pi. Which is 113097.3355 Joules.
Apparently, that is wrong. What am I doing wrong?