Calculus

posted by .

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 -

    did you make a sketch??
    let the radius of the cylinder be r
    let the height of the cylinder by h

    by similarity I can set up the ratio h/(2-r) = 8/2
    ---> h = 8-4r

    volume of cylinder
    = pi(r^2)(8-4r)
    = 8pi(r^2) - 4pi(r^3)

    differentiate, set equal to zero, solve for r, etc

    (I got r = 4/3)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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?
  2. 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?
  3. Calculus

    A right circular cylinder is inscribed in a cone with height h and base radius r. Find the largest possible surface area of such a cylinder.
  4. 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?
  5. 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?
  6. 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?
  7. 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.
  8. 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?
  9. 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?
  10. 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?

More Similar Questions