# Maths

Watch
Announcements
This discussion is closed.
#1
the last question of my assignement (10 questions) which I have managed to complete 9 (with the help of this forum) - this one has stumped me

A can of orange juice is in the form of a right-circular cylinder and holds a volume of 1000 cm^3 of fluid. what dimensions of the can will give the smallest surface area?

i've worked this out:

Pi * r^2 * h = 1000
S.A Top = Pi * R^2
S.A Bottom = Pi * R^2
+ Cylinder Wall = 2 * Pi * r * h

Surface Area Total = Pi * R^2 + Pi * R^2 + 2 * Pi * R * H

Volume = Pi * r ^ 2 * h
Volume = 1000
Height = 1000 / (pi * r ^ 2)

SA(r) = 2*pi*r^2 + 2000/r

but dont know where to go from here - can anyone help? This is my last assignemnt for the year! Happy dayz

Louk
0
16 years ago
#2
Whatsa right circular cylinder?
0
#3
no idea - just how the question is phrased

I assume it means a normal cylinder

Louk
0
16 years ago
#4
I had a go, and seem to have found a maximum surface area. But no minimum.
0
#5
Cool - How did you get that??

Louk
0
16 years ago
#6
Volume = (Pi)r^2(h) = 1000

h= 1000/(pi*r^2)

Surface Area = 2(pi)r^2 + 2(pi)rh

Substitute expression for H into formula:
S.A. = 2(pi)r^2 + 2(pi)r* (1000/(pi)r^2)

Then differentiate this formula (now only one unknown - r)and find a minimum turning point.
Use this value for r to calculate the dimensions.

Hope this helps!
0
16 years ago
#7
I just did it very quickly, so may have made a mistake, but I got
r=5.42
h=10.84
0
16 years ago
#8
(Original post by hitchhiker_13)
I just did it very quickly, so may have made a mistake, but I got
r=5.42
h=10.84

Thats right!
0
16 years ago
#9
(Original post by Louk)
Cool - How did you get that??

Louk
Dunno, must have went wrong somewhere. 0
16 years ago
#10
(Original post by Ralfskini)
Thats right!

Well yay for me! 0
16 years ago
#11
(Original post by Louk)
the last question of my assignement (10 questions) which I have managed to complete 9 (with the help of this forum) - this one has stumped me
Which level of Maths are you doing?

In general when you want to find maximum and minimum points of a function you first find the derivative of the function and then solve for 0. This point will then be a maximum or a minimum. That this is teh case can easily be illustrated by considering the motion of a stone throw vertically upwards into the air. At the moment the stone has reached its highest point it is (for an infinetely small amount of time) standing still. AFter that it starts moving down. The derivative pf the stones position with respect to time is zero when the stone has just reached its highest point.

Examples:

Find the maximum/minimum of the following functions:

F(x) = -x²
G(x) = x² + x + 4
H(x) = sin(x)

Solutions:

F'(x) = -2x = 0
Hence x = 0.

G'(x) = 2x + 1 = 0
Hence x = 1/2

H'(x) = cos(x) = 0
Hence x = 90 degrees = 0.5pi radians

I am not going to explain how to find the function for the surface area as a function of r as others have already done so, but once this function has been found this is the procedure to follow.
0
16 years ago
#12
i dont understand how H(x) = sin x => H'(x) = cos x
actually im kinda lost on the whole equation from start to finish, H(x) ~
0
16 years ago
#13
(Original post by Revelation)
i dont understand how H(x) = sin x => H'(x) = cos x
actually im kinda lost on the whole equation from start to finish, H(x) ~
H'(x) is the derivative of H(x)...
0
16 years ago
#14
(Original post by Revelation)
i dont understand how H(x) = sin x => H'(x) = cos x
actually im kinda lost on the whole equation from start to finish, H(x) ~

its a long and boring proof. dont worry about it.
0
X
new posts Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### Poll

Join the discussion

#### If you do not get the A-level grades you want this summer, what is your likely next step?

Take autumn exams (130)
46.59%
Take exams next summer (40)
14.34%
Change uni choice through clearing (69)
24.73%
Apply to uni next year instead (26)
9.32%
I'm not applying to university (14)
5.02%