Posted by rolan on Monday, August 13, 2012 at 12:32pm.
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 - Steve, Monday, August 13, 2012 at 2:48pm
You are ok up to your last line:
[(12-h)/2]^2 = (144-24h+h^2)/4
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
- math - Anonymous, Monday, January 11, 2016 at 3:41pm
Answer This Question
More Related Questions
- Calculus - Given a right circular cone, you put an upside-down cone inside it so...
- Calculus: Optimization - I have no idea how to approach this problem, if someone...
- calculus - Given a right circular cone, you put an upside-down cone inside it so...
- maths - Two spheres of radius 6 cm and 4cm are inscribed in a right circular ...
- Math - An inverted right cone, half filled with water. I've only the volume of ...
- geometry math - There is an upside-down cone that is 12m high and has a circular...
- Math - Please Help A body consists of a solid hemisphere of radius r joined to a...
- Geometry - One right circular cone is set inside a larger circular cone. The ...
- Math - A sphere is inscribed in a right cone. The slant height of the cone = the...
- Calculus - A cone is inscribed in a sphere of radius a, centred at the origin. ...