Friday

August 29, 2014

August 29, 2014

Posted by **ali** on Saturday, July 12, 2014 at 12:08am.

- mathe -
**MathMate**, Saturday, July 12, 2014 at 6:21amLet the cone radius = R

cone height = H

Let cylinder height = h

then cylinder radius, r = R(1-h/H)

Volume of cylinder, V

=πr²h

=πR²(1-h/H)²h

For maximum volume,

dV/dh=0

π(1-h/H)^2R^2-(2πh(1-h/H)R^2)/H=0

which simplifies to:

(H^2-4hH+3h^2)=0

which when solved for h gives

h=H/3 or h=H

h=H will give a zero volume (min.) so reject.

for h=H/3,

Volume of cylinder

=πR²(1-(H/3)/H)²(H/3)

=πR²(2/3)²(H/3)

=(2/3)²(πR²H/3)

=4/9 volume of the cone.

**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 ...

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 ...

Calculus - Given a right circular cone, you put an upside-down cone inside it so...

Geometry - Infinitely many different sectors can be cut from a circular piece of...

geometry - 11. Infinitely many different sectors can be cut from a circular ...