You are asked to build an open cylindrical can (i.e. no top) that will hold 171.5 cubic inches. To do this, you will cut its bot tom from a square of metal and form its curved side by bending a rectangular sheet of metal.
1 answer:
<span>Generate a function for the height of the cyliner as a function of radius. Use this function to generate a function of r for the material used. Take the derivative of that function, set it to zero, and solve for r.
</span><span>V=π<span>r2</span>h</span>h=d
h=d=2r
h=2r
<span>V=π<span>r2</span>2r
</span><span>V(r,h)=180.5=π<span>r2</span>h⟹h=<span>180.5/<span>π<span>r2</span></span></span></span><span>⟹A(r)=r(r+h)=<span>r2</span>+<span>180.5/<span>πr
</span></span></span><span>A(r)=2r(2r+h)=4<span>r2</span>+<span>361/<span>πr
</span></span></span>
<span><span>A′</span>(r)=8r−<span>361/<span>π<span>r2</span></span></span></span>
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For steps, use this link:
https://mathsolver.microsoft.com/en/solve-problem/64705%20%60div%20%20386
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