1. Questions

Math

Q)
'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!

SA1=

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



For Further Reading

Math - Reiny, Friday, November 9, 2007 at 10:45pm
your line
SA=2Pi r^2 + 2 Pi r (1131.97/Pi r^2)

reduces to

SA=2Pi r^2 + 2263.94/r

then

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

now set this equal to zero for a minimum surface area, so....do 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???)

Math - Josh, Saturday, November 10, 2007 at 12:09am
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
thanks

  1. 👍 0
  2. 👎 0
  3. 👁 152
Josh

  1. I gave you all the steps for the solution.
    The only thing I didn't do was to take the cube root to get your final answer.
    (BTW, I did give you the answer)

    Usually we do not do a students homework or assignment questions in full detail.
    Surely if you are enrolled in a Calculus course you should be able to provide the missing steps for such a routine question.

    1. 👍 0
    2. 👎 0
    Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

  2. 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

  3. 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

  4. 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?

  1. 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

  2. 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

  3. physics

    A small cylinder rests on a circular turntable that is rotating clockwise at a constant speed. The cylinder is at a distance of r = 12 cm from the center of the turntable. The coefficient of static friction between the bottom of

  4. Calculus

    For a cylinder with a surface area of 90, what is the maximum volume that it can have? Round your answer to the nearest 4 decimal places. The volume of a cylinder is πr^2*h and the surface area is 2πrh+2πr^2.

  1. Algebra

    The volume of a right circular cylinder (think of a pop can) is jointly proportional to the square of the radius of the circular base and to the height. For example, when the height is 10.62 cm and the radius is 3 cm, then the

  2. Calculus - Optimization

    A parcel delivery service a package only of the length plus girth (distance around) does not exceed 24 inches. A) Find the dimensions of a rectangular box with square ends that satisfies the delivery service's restriction and has

  3. 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.

  4. 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?

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