"Pie?".. So, it has to do with baking pies?.
I have a q..bin with volume pie/8m^3 made from metal, to keep costs low it should have the min possible surface area, Am^2.
* using pie/8m^3 write an expression for height t in terms of radius r..
Which iv done pie/8m=pier^2Xh, then , pie/8 - pier^2=h, then, pie/8pie r^2=h, then, 1/8r^2=h, is this write?
then show this expressen as A=pier^2+pie/4r
area of base= pier^2
curved area side hX2pier=2pie r h
total area pier^2+2pie r h
pie r^2+2 pie r 1/8r^2
and finally A=pie r ^2+ pie/4r is this right?
then it says to find dA/r and d^2A/dr^2
which i have done 2pier-pie/4r^2 then 2pie+pie/2r^3
But finally i need to find the corresponding minimum values..but im not sure how too so this....
can you tell me how please?
Thank you
It's spelled 'Pi'. I had to, I'm sorry.
I assume when you say radius, the bin is cylindrical?.
I can tell you that the surface area is minimum when the height equals the diameter.
We have ...[1]
The surface area, assuming the bin has a top and bottom, would be
...[2]
This is what must be minimized.
So, we solve [1] for h andf sub into [2]:
Solving [1] for h, we get
That goes into the surface formula:
Differentiate:
Set to 0 and solve for r and we get
Plug that into h and it should be twice that.
Sure enough. So, the surface area is minimum when the height equals the diameter.