Posted by ali on Saturday, July 12, 2014 at 12:08am.
Show that a right-circular cylinder of greatest volume that can be inscribed in a right-circular cone that has a volume that is 4/9 the volume of the cone.
- mathe - MathMate, Saturday, July 12, 2014 at 6:21am
Let the cone radius = R
cone height = H
Let cylinder height = h
then cylinder radius, r = R(1-h/H)
Volume of cylinder, V
For maximum volume,
which simplifies to:
which when solved for h gives
h=H/3 or h=H
h=H will give a zero volume (min.) so reject.
Volume of cylinder
=4/9 volume of the cone.
Answer This Question
More Related Questions
- Calculus - Show that a right-circular cylinder of greatest volume that can be ...
- Math - Calculus I - Optimization Problem: Find the dimensions of the right ...
- math - A right circular cone is inscribed inside a sphere. The right circular ...
- Calculus - A right circular cone is inscribed in a sphere of radius r. Find the...
- Calculus - A right circular cone is inscribed in a sphere of radius r. Find the ...
- Maths - A right circular cone is circumscribed about a sphere of radius a .If h ...
- Calculus - Find the radius, volume, and hieght of the right- circlar cylindar ...
- Math - A right circular cylinder with a height of 20 cm and a right circular ...
- Maths - “A solid consists of a right circular cylinder surmounted by a cone of ...
- Calculus - Given a right circular cone, you put an upside-down cone inside it so...