geometry math

There is an upside-down cone that is 12m high and has a circular base with a radius of 4m that is being filled with liquid. Make V, the volume, a function of the height of the liquid, h. What is the volume of the cone when the water is 5m deep?

V = (1/3)pi*r^2*h
This formula doesn't help cuz the cone is upside-down. Is there another formula?


Actually,
V = (1/3)pi*r^2*h
is correct for the volume of liquid in an upside-down cone, if h is the liquid depth, measured from the tip at the bottom. In this case, r = (h/3) is the radius of the pool of liquid inside when the liquid is h deep. r is a function of h.
Therefore
V = (1/9)pi*h^3
Plug in h = 5 for the volume when the water is 5m deep.

V = Pir^2h/3

The volume of the entire cone is V = 3.14(4^2)12/3 = 201.06

Too find the volume when the water level is 5 ft., you must subtract the volume of the cone above the 5 ft. level or a cone of 7 ft. height and a base radius of 4 - 1.666 = 2.333 ft.

V(5) = 201.06 - 3.14(2.333^2)7/3 = 161.16 cub.ft.

  1. 👍 0
  2. 👎 0
  3. 👁 147

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the center of the base of the larger cone, and its base is parallel to the base of the larger cone. If you choose the upside-down cone to

    asked by Mishaka on December 16, 2011
  2. calculus

    Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the center of the base of the larger cone, and its base is parallel to the base of the larger cone. If you choose the upside-down cone to

    asked by Mari on January 21, 2012
  3. Calculus: Optimization

    I have no idea how to approach this problem, if someone knows just how to relate h, r with H,R, that would be extremely helpful and I can workout the rest! Thank you in advance. Given a right circular cone, you put an upside-down

    asked by Jazz on February 17, 2015
  4. math

    Two right circular cone, one upside down in the other. The two bases are parallel. The vertex of the smaller cone lies at the center of the larger cone’s base. The larger cone’s height and base radius are 12 and 16 ft,

    asked by rolan on August 13, 2012
  5. math geometry

    A right circular cone has a base diameter of 10 and a height of 18. A second right circular cone has a base diameter of 15. If the volume of the second cone is equal to the volume of the first cone, then what is the height of the

    asked by k on December 19, 2017
  6. calculus

    Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile

    asked by remy on May 14, 2012
  7. Related Rates

    Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile

    asked by Anonymous on March 1, 2017
  8. Calculus

    Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile

    asked by Nathan on October 9, 2013
  9. calculus

    Gravel is being dumped from a conveyor belt at a rate of cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other. How fast is the height of the

    asked by Anonymous on November 4, 2012
  10. Math

    Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile

    asked by Ramin on October 10, 2017

More Similar Questions