math

posted by .

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, respectively. What are the smaller cone’s height (h) and base radius (r), both are in ft, that maximize the smaller cone’s volume?

my answer :

R = radius of bigger cone = 6 ft
r = radius of smaller cone…?
H = height of bigger cone = 12 ft
h = height of smaller cone?

r/R = H-h/H
r/6 = 12-h/12
r = 12-h/2

V = 1/3 r^2h
= 1/3 (12-h/2)^2 h
= 1/3 (144-h^2/4) h

Please help me to complete this assignment…

  • math -

    You are ok up to your last line:
    [(12-h)/2]^2 = (144-24h+h^2)/4

    so,

    v = pi/12 (144h-24h^2+h^3))

    dv/dh = pi/12(144-48h+3h^2)
    dv/dh=0 when h=4,12

    Naturally, v=0 when h=12, so
    v(4)=64pi/3

  • math -

    V=64Pi/3
    h=4,12

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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 …
  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 have …
  3. 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 have …
  4. maths

    Two spheres of radius 6 cm and 4cm are inscribed in a right circular cone.The bigger sphere touches the smaller one and also the base of cone .find the height of the cone?
  5. Geometry

    One right circular cone is set inside a larger circular cone. The cones share the same Axis, the same vertex, and the same height. Find the volume of the space between the cones of the diameter of the inside cone is 6in., the diameter …
  6. Math

    An inverted right cone, half filled with water. I've only the volume of the entire cone to go from. So the volume of the cone = 1/3 the base area * height I've been told by a friend that the base area of a half scale cone = 1/4 of …
  7. 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 cone …
  8. Math

    Please Help A body consists of a solid hemisphere of radius r joined to a right circular cone of base radius r and perpendicular height h. The plane surfaces of the cone and hemisphere coincide and both solids are made of the same …
  9. PLEASE HELP

    Find the volume of a cone of height 8 centimeters and base radius 6 centimeters. This cone is sliced by a plane that is parallel to the base and 2 centimeters from it. Find the volumes of the two resulting solids. One is a cone, while …
  10. Math

    Thevolume of a right circular cone is 5 litres.calculate the volumes of the two parts into which the cone is divided by a plane parallel to the base,one-third of the way down from the vertex to the base.

More Similar Questions