Calculus

Consider a hemispherical bowl with a radius of 12 cm. The bowl contains water to a depth of 9 cm. The density of the water at any point x cm below the surface of the water is given by 2e^(0.15x) g/cm^3.

A. Find the volume of the water in the bowl.
B. Find the mass of the water in the bowl.
C. Suppose that the bowl is covered and then inverted and that no water is lost in the process. Find the depth of the water in the inverted bowl.

Show steps if possible please

  1. 👍 0
  2. 👎 0
  3. 👁 62
asked by Roy
  1. A. The volume of a spherical cap of height h of a sphere of radius r is
    V = π/3 h^2(r-h)
    This is a known formula, but you can always verify it by finding the volume made by rotating a circular segment. For example,
    V = ∫[h,r] π(r^2-y^2) dy

    B. The mass of any small disc of water is its area times its density.
    So, integrating again, with x=r-y,
    M=∫[h,r] π(r^2-y^2) *2e^(0.15(r-y)) dy

    C. Subtract the volume for (A) from 2π/3 r^3 and solve for h in the volume formula.

    1. 👍 0
    2. 👎 0
    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. pope john

    A hemispherical bowl of radius 6cm contains water which is flowing into it at a constant rate.When the height of the water is h cm the volume V of water in the bowl is given by V=22/7(6h^2-1/3h^3)cm^3.Find the rate at which the

    asked by function on September 15, 2016
  2. This math question is confusing.

    A set of hemispherical bowls are made so they can be nested for easy storage. The largest bowl has a radius of 30 cm and each successive bowl has a radius 90% of the preceding one. What is the radius of the tenth bowl? there is a

    asked by Emily on January 4, 2016
  3. Physics

    A hemispherical bowl of radius R is rotated about its axis of symmetry which is kept vertical. A small block is kept in the bowl at a position where the radius makes an angle Θ with the vertical. The block rotates with the bowl

    asked by Kewal on January 2, 2012
  4. calcus

    water partially fills a hemispherical bowl of radius 40cm so that the depth of the water is 20 cms. write down an integral representing the volume of the water in the bowl

    asked by john on April 14, 2016
  5. Calculus

    An open hemispherical bowl of radius R is slowly draining through a small hole of radius r in the bottom of the bowl. Let g be the acceleration due to gravity and y be the depth of the water (which means the distance from the

    asked by chamy on April 8, 2012
  6. Calculus

    Consider a hemispherical bowl of radius 10cm. (4 points) If the water level in the bowl is h cm deep, find the radius of the surface of the water as a function of h. (6 points) The water level drops at a rate of 0.1 cm per hour.

    asked by Karina on December 2, 2012
  7. Math

    If a hemispherical bowl of radius 6cm contains water to a depth of h cm, the volume of the water is 1/3πh^2(18-h). Water is poured into the bowl at a rate 4 cm^3/s . Find the rate at ehich the water level is rising when the depth

    asked by Marney on September 16, 2012
  8. Math

    A fish bowl is constructed out of a spherical bowl with diameter 20cm. The bowl was initially empty and water flows into the bowl at a rate of 10cm^3/s. Let V and h be the volume and depth of water in the bowl at time t seconds

    asked by Isabel on November 30, 2016
  9. PHYSICS

    A 2.5 g ice flake is released from the edge of a hemispherical bowl whose radius r is 40.0 cm. The flake-bowl contact is frictionless. (a) What is the speed of the flake when it reaches the bottom of the bowl? (b) If a second

    asked by Anonymous on October 21, 2011
  10. Math

    Yan water leaks from a hemispherical bowl of 8 cm diameter at the rate of 10 cm per hour .How fast is the surface falling when the water is 2 cm deep in the bowl

    asked by Yan on September 9, 2015

More Similar Questions