'What are the dimensions of a cylinder that has the same maximum volume as the box (1131.97 cm2), but uses the minimum amount of material to make it?'

Here are the notes I have so far:

SA=2Pi r^2 + 2 Pi r (1131.97/Pi r^2)

Now i need to use derivatives, I don't know how!


Then these notes-
at min. gradent =0 therefore SA1=0

rearrange to find r

sub r in to find

Anyone have any clue? thanks. its my assinment

  1. 👍
  2. 👎
  3. 👁
  1. your line
    SA=2Pi r^2 + 2 Pi r (1131.97/Pi r^2)

    reduces to

    SA=2Pi r^2 + 2263.94/r


    SA' = 4(pi)r - 2263.94/r^2

    now set this equal to zero for a minimum surface area, the algebra

    r^3 = 2263.94/(4pi)

    = 180.15862

    take the cube root to get r,

    go back into 1131.97/(Pi r^2) to get the height

    (I got h = 11.296 and r = 5.648
    notice that would make the diameter equal to the height, mmmmhhhh?
    isn't Calculus wonderful???)

    1. 👍
    2. 👎
  2. you couldn't show all the working could you? its just that i don't understand how to do them, and can't do them

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    An open box of maximum volume is to be made from a square piece of cardboard, 24 inches on each side, by cutting equal squares from the corners and turning up the sides to make the box. (a) Express the volume V of the box as a

  2. Pre-Calc

    A rectangular package to be sent by a delivery service can have a maximum combined length and girth (perimeter of a cross section) of 120 inches. a. Show that the volume of the package is V(x)= 4xsquared(30-x) b. Use your graphing

  3. calculus

    A cylinder is generated by rotating a rectangle with perimeter 12 in. about one of its sides.? Express the volume of the cylinder as a function of x. Find the approximate value of x that maximizes the volume. Then give the

  4. Chemistry

    the mass of cylinder one is 1.35 times the mass of cylinder two, and the volume of cylinder one is 0.792 times the volume of cylinder two. If the density of cylinder one is 2.70 g/cm3 what is the density of cylinder two? THIS

  1. 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.

  2. Math 8th grade algerbra

    a cylinder has a radius of 3cm and a length of 10cm every dimention of the cylinder is multiplied by 3 to form a new cylinder how is the ratio of the volumes related the ratio of corresponding dimensions? how would i do this?

  3. 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?

  4. Math

    The table on the right shows the measured dimensions of a rectangular prism and the minimum and maximum possible dimensions based on the greatest possible error. What is the greatest possible percent error in finding the volume of

  1. geometry

    The diameter and height of this cylinder are equal to the side length, S, of the cube in which the cylinder is inscribed. What is the expression for the cylinder's volume?

  2. Math

    Suppose Cylinder A has the same height but twice the radius of Cylinder B. What is the ratio of the volume of Cylinder B to Cylinder A?

  3. College Chemistry

    If the density of cylinder 1 is 3.55 , what is the density of cylinder 2? (The masses and volumes of two cylinders are measured. The mass of cylinder 1 is 1.35 times the mass of cylinder 2. The volume of cylinder 1 is 0.792 times

  4. Math HELP

    The table below shows the measured dimensions of a prism, and the maximum and minimum possible values based on the greatest possible error. Dimensions l w h Measured 9 5 3 Maximum 9.5 5.5 3.5 Minimum 8.5 4.5 2.5 a. Find the

You can view more similar questions or ask a new question.