maths

A spherical tank in a petro-chemical plant has a radius of 5m.
Give an expression which, when integrated from y=-r to
y=d-r ,will give the volume of liquid in the tank where r is
the radius and d is the depth of liquid.
If liquid is entering the tank at a rate of 1500 litres per second and
the depth is 3m how long will it take to fill the tank? Give your
answer in seconds.

  1. 👍 0
  2. 👎 0
  3. 👁 76
asked by URGENT
  1. The volume of a thin slice of water is the area of the slice times its thickness, dy

    At a depth of d, with d<r, we have
    the radius of the surface of the water is x = √(r^2-y^2)
    v = ∫[-r,d-r] π(r^2-y^2) dy

    Now you can answer the last part by subtracting the volume from the whole sphere's volume of 4/3 pi * 5^3 and dividing by 1500L/s = 1.5 m^3/s

    1. 👍 0
    2. 👎 0
    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. Maths, physics, science

    A spherical tank in a petro-chemical plant has a radius of 5m. If liquid is entering the tank at a rate of 1500 litres per second and the depth is 3m how long will it take to fill the tank? Give your answer in seconds.

    asked by URGENTTTT on May 16, 2018
  2. Math - Calculus

    Im doing some practice questions and im stumped on this one. The amount of cleaning fluid in a partially filled, spherical tank is given by V = (pi)R(h^2)-(pi(h^3))/3 Where R is the radius of the rank, and h is the depth of the

    asked by Swk13 on December 3, 2006
  3. numerical methods

    Consider a spherical storage tank containing oil. The tank has a diameter of 8 ft. You are asked to calculate the height h to which a dipstick 10 ft long would be wet with oil when immersed in the tank when it contains 6 3 ft of

    asked by aira on April 23, 2015
  4. math

    the radius of a spherical tank 0.7 meter. how many liters of water can the tank hold?

    asked by rachel on August 18, 2012
  5. Ps 327x math

    A spherical tank has a radius of 60 centimeter. Find the maximum volume of water the tank can hold.

    asked by Tyrell on November 22, 2015
  6. calculus2

    A tank is full of water. Find the work required to pump the water out of the spout. (Use 9.8 m/s^2 for g. Use 1000 kg/m^3 as the density of water. Assume r = 9 m and h = 3 m.) The tank is a spherical shape with r as the

    asked by A on June 28, 2018
  7. maths

    A spherical tank of diameter 3m is filled with water from a pipe of radius 30cm at 0.2m/s.calculate an corect to 3s.f the time in minute it take to fill the tank.thankyou godbless

    asked by anthony on July 28, 2015
  8. maths

    here is another.A spherical tank of diameter 3m is filled wit water from a pipe of radius 30cm to 0.2m/s.calculate an corcet to 3s.f the time in minute it wil take to feel the tank take to be TT=22/7 thankyou

    asked by anthony on July 28, 2015
  9. Physics ASAP PLease

    A spherical capacitor consists of a spherical conducting shell of radius b and charge -Q concentric with a smaller conducting sphere of radius a and charge +Q . Enter an expression for the capacitance of this device in terms of

    asked by asha on November 6, 2013
  10. math

    a spherical fishtank has radius of 25 cm. The tank is filled with water with a depth of 20 cm. By using integral find the volume of the water inside the tank.

    asked by ibranian on August 7, 2012

More Similar Questions