Calculating Work to Fill a Spherical Tank of Water with Given Parameters

[kari82]

Hello, Can someone please give some hints on how to start this problem? I tried a few things but nothing is working!

A spherical tank of water has a radius of 14 ft, with the center of the tank 50 ft above the ground. How much work will it take to fill the tank by pumping water up from ground level? Assume the water weighs 62.4 lb/ft3. Give your answer to the nearest ft · lb.

So this is what I did:

I know that we need to use this formula W=wpi∫x^2deltay

if i take that the center is 50 ft above the ground that means i can use point (0,50) to find x^2 and r=14 (here is where i think I am wrong)

(x-h)^2+(y-k)^2=r^2 ==> x^2=14^2-(y-50)^2
deltay=(28-y)
and we should integrate from y=36 to y=64 because the center of the tank is 50ft above the ground?

Please help!

 

[lippyka]

You are on the right track! You have correctly identified the formula, variables, and points you need to solve this problem. The next step is to calculate the integral. To do this, you should use the substitution u = y - 50, so that the integral becomes wpi∫(14^2-u^2)du. Then, you can evaluate the integral from u = 36 - 50 to u = 64 - 50 and multiply this result by wpi.