Math. HELP!

posted by .

A cylinder is to be made of circular cross-section with a specified volume. Prove that if the surface area is to be a minimum, then the height of the cylinder must be equal to the diameter of the cross-section of the cylinder.
Maybe it's the wording, but I have not been able to crack this one for the past half-hour!

  • Math. HELP! -

    let the radius be r and the height be h
    let the volume be V, where V is a constant
    πr^2h = V
    h = V/(πr^2)

    Area = 2 circles + rectangle
    = 2πr^2 +2πrh
    = 2πr^2 + 2πr(V/πr^2)
    = 2πr^2 + 2V/r
    d(Area)/dr = 4πr - 2V/r^2
    = 0 for a max/min of area
    4πr = 2V/r^2
    r^3 = V/(2π) = πr^2h/2π
    r = h/2
    or
    2r = h
    diameter = height !!!!

  • Math. HELP! -

    Reiny. You. Are. God. Thank you :D

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Maths help

    Hi MY question is if a cylinder has a volume of 72cm cubed and a cross-sectional area of 18cm squared. Work out the height of the cylinder Can someone show me how we do it by the steps The cross-section of a cylinder is a circle. so …
  2. maths help

    Hi MY question is if a cylinder has a volume of 72cm cubed and a cross-sectional area of 18cm squared. Work out the height of the cylinder Can someone show me how we do it by the steps The volume of a cylinder is given by volume = …
  3. Math. HELP!

    A cylinder is to be made of circular cross-section with a specified volume. Prove that if the surface area is to be a minimum, then the height of the cylinder must be equal to the diameter of the cross-section of the cylinder. Maybe …
  4. Math

    A cylinder is to be made of circular cross-section with a specified volume. Prove that if the surface area is to be a minimum, then the height of the cylinder must be equal to the diameter of the cross-section of the cylinder. Maybe …
  5. Math. HELP!

    A cylinder is to be made of circular cross-section with a specified volume. Prove that if the surface area is to be a minimum, then the height of the cylinder must be equal to the diameter of the cross-section of the cylinder. Maybe …
  6. math

    A container in the shape of a right circular cylinder with no top has surface area 3*pi (m2). What height h and base radius r will maximize the volume of the cylinder ?
  7. math

    A right circular cylinder has a diameter of 16 mm and a height of 12 mm. What is the surface area of the cylinder?
  8. Math - Please Help

    The surface area of a right circular cylinder is 1200 cm^2 . If the height of the cylinder is twice its diameter, find the dimensionsof the cylinder. I know th formula for SA is SA = 2pir^2 + 2pirh I know h = 2d. I know r = 1/2 d What …
  9. maths

    A hallow sphere has a volume of xcm^3 and a surface area of ycm^2 if the value of the diameter of the sphere is the radius of the area of a semicircle.what is the radius of a cylinder(P) if the area of the circle is equal to the area …
  10. tech math

    Each cylinder bore of a cylinder engine has a diameter of 2.50in. and a height of 4.90 what is the combined total surface area of all four cylinder?

More Similar Questions