Ask Me Help Desk

Ask Me Help Desk (https://www.askmehelpdesk.com/forum.php)
-   Mathematics (https://www.askmehelpdesk.com/forumdisplay.php?f=199)
-   -   Cylindrical tank equation help (https://www.askmehelpdesk.com/showthread.php?t=51022)

  • Dec 29, 2006, 07:38 AM
    WHITEO
    Cylindrical tank equation help
    A cylindrical tank has been buried underground in a horizontal position. The length of the tank is 30 feet, and the diameter of the tank is 16 feet. The volume of the liquid in the tank is calculated by measuring the depth of the liquid in inches with a long stick. Write a general formula for the volume of the cylinder (answer in cubic feet) in terms of d, the depth of the liquid.









    Sample Depths and Volumes

    Depth (in.)Volume (cu. ft.)
    9 in. 102.449 ft3
    15 in. 218.291 ft3
    51 in. 1284.211 ft3
    60 in. 1610.429 ft3
    96 in. 3015.929 ft3
    117 in. 3849.181 ft3
    132 in. 4421.429 ft3
    141 in. 4747.647 ft3
    164 in. 5487.221 ft3
    192 in. 6031.858 ft3
  • Dec 29, 2006, 08:25 AM
    galactus
    I assume you're required to use calculus.

    Center the end of the tank at the origin.

    Use the equation of a circle to construct a integral.

    The radius of the tank is 8 and the height is 30.



    Perform the integration and you have a formula for the volume in terms of d(the depth).

    For the integration, trig substitution may be a good approach. Let





    Remember,





    Don't forget to change the limits of integration:





    So, you have:



    Now use the identity:



    =

    Now use your limits of integration to derive the frmula you need.

  • All times are GMT -7. The time now is 03:26 PM.