Business Calculus
A cylinder is inscribed in a right circular cone of height 8 and radius (at the base) equal to 8. What are the dimensions of such a cylinder which has maximum volume?
asked by
Daniela Davila

Let r be the radius of the inscribed cylinder. The top edge of the cylinder (where the height is h) must touch the cone, where h and r are related by the straightline equation
h = 8  r.
The volume of the cone is
V (r) = pi*r^2 h = pi*r^2*(8r)
= pi*[8 r^2  r^3]
When the cylinder's volume is a maximum, dV/dr = 0, so
16r = 3r^2
r = 16/3, which is 2/3 the height of the come.
posted by drwls
Respond to this Question
Similar Questions

Calculus
A cylinder is inscribed in a right circular cone of height 6.5 and radius (at the base) equal to 6. What are the dimensions of such a cylinder which has maximum volume? 
Calculus
A cylinder is inscribed in a right circular cone of height 5.5 and radius (at the base) equal to 7. What are the dimensions of such a cylinder which has maximum volume? 
Math: Calculus
A cylinder is inscribed in a right circular cone of height 3.5 and radius (at the base) equal to 7. What are the dimensions of such a cylinder which has maximum volume? 
Calculus
A cylinder is inscribed in a right circular cone of height 8 and radius (at the base) equal to 2. What are the dimensions of such a cylinder which has maximum volume? Radius? Height? 
Calculus
A cylinder is inscribed in a right circular cone of height 5.5 and radius (at the base) equal to 2 . A) What are the dimensions of such a cylinder which has maximum volume? B) What is the radius? C) What is the height? 
Math  Optomization
A cylinder is inscribed in a right circular cone of height 6.5 and radius (at the base) equal to 5.5. What are the dimensions of such a cylinder which has maximum volume? 
Math
A cylinder is inscribed in a right circular cone of height 8 and radius (at the base) equal to 2.5. What are the dimensions of such a cylinder which has maximum volume? What is the radius, and height? 
math!
A cylinder is inscribed in a right circular cone of height 8 and radius (at the base) equal to 5. What are the radius and height of such a cylinder which has maximum volume? 
calculus
Find the maximum volume of right circular cylinder that can be inscribed in a cone of altitude 12 cm and base radius 4 cm, if the axes of the cylinder and con coincide. 
Geometry
A cone has diameter 12 and height 9. A cylinder is placed inside the cone so the base of the cylinder is concentric with the base of the cone and the upper base of the cylinder is contained in the surface of the cone. If the