Integration problem, cylindrical water tank

A cylindrical water tank with radius 2m is installed in such a way that the axis is horizontal and the circular cross sections are vertical. Water is put into the tank so that the depth of the water is 3m. What percentage of the total capacity of the tank is being used? Round off to the nearest percentage point.

I have tried computing the integral of V= (2pix(4-x^2)^.5)dx where I got -(1/3)cos^3x ... I am unsure as to what else I have to do. I am completely lost on this problem.

Re: Integration problem, cylindrical water tank

Hey kyliealana.

Do you have information on the height of the tank? If what you say is correct, the tank is aligned on the ground where the x and z axes are parallel to the circular cross sections which means that in this case, volume is calculated as pi*r^2*h for some height h.

Can you help us with regards to the height?

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Re: Integration problem, cylindrical water tank

Attachment 29163

This is what I have so far and I feel like I am really off track.

Re: Integration problem, cylindrical water tank

Please do not double post. See the original thread here.

-Dan