Question

A cylindrical containet with base is to hold 64inch^3. find the dimension so that the surface area of meatal required is minimum when the container is 1) open can 2) closed can​

Answer 1

Let's do it step by step. We want to minimize SA=2πr2+2πrh, with the constaint πr2h=128π. The constraint gives us h=128/r2. So we can look at SA as a function of r:

SA(r)=2πr2+2π128r⟹SA(r)=2πr2+256πr.

To find the critical point, we solve SA′(r)=0, that is:

4πr−256πr2=0⟹r−64r2=0⟹r3=64⟹r=4.

Now:

SA(4)=2π(4)2+2π1284=32π+2π⋅32=32π+64π=96π.

Answer 2

Answer:

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