Question

hello , i have no idea on how to solve this question again... somebody pls help me asap.... i need u here with me now...pls pls pls

Right circular cylindrical tin cans are to be manufactured to contain a given volume .The end pieces of the can are cut out from square pieces of tin with the corners wasted. If h is the height of the can and r its radius

a)write down the least area of tin required (including the waste) in the making of each can.
b)determine the ratio of the height to diameter for the most economical production..

Answer 1

krik krik

Answer 2

Is there a given volume?

Answer 3

I have been toying around with this problem and I feel like some information is missing.

@Ika_Kim, are you sure that you have provided all the information?

Answer 4

id assume the volume given is some constant K and work it from there

Answer 5

@amistre64 this is as far as I got

Answer 6

Vc = pi r^2 h = K

h = K/(pi) r^-2
h' = -2K/(pi) r^-3

Sac = 2pi r^2 + 2pi r h
S'ac = 4pi r + 2 pi r h' + 2h pi = 0

subbing in h' and h

4pi r + 2 pi r -2K/(pi) r^-3 + 2pi K/(pi) r^-2 = 0

we can solve for r

Answer 7

2pi r -K r^-2 = 0

2pi r = K r^-2

r^3 = K/(2pi)

r = cbrt(K/(2pi))

with any luck

Answer 8

the least area of tin will then be the amount of area of the squares for the lids, and not the circles; or simply 8r^2

Answer 9

@stamp , do you agree?

Answer 10

The measurement of the lids depends on the dimensions of the square, so they are related in that sense.

Answer 11

sorry guys , i am so so sure that there is no additional information other than above

Answer 12

thank you for helping me !