anonymous
  • anonymous
A paper drinking cup is being designed in the shape shown in the accompanying figure. The amount of paper needed to manufacture the cup is determined by the surface area S of the cup, which is given by s=πr√(r^(2))+h^(2) where r is the radius and h is the height. (b) Could the formula for S be simplified as follows? πr√(r^(2))+h^(2)=πr(√(r^(2))+√(h^(2)))=πr(r+h)
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Nonono. In general \[\sqrt{a + b}\ \not= \sqrt{a} + \sqrt{b} \]
anonymous
  • anonymous
Could you explain your answer to me Mr. Newton?
anonymous
  • anonymous
That simplification uses the assumption I listed above (splitting it up into two roots) The assumption is false.

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anonymous
  • anonymous
Hmmm
anonymous
  • anonymous
It probably got confused with \[\sqrt{a\times b} = \sqrt{a} \times \sqrt{b} \] which is true.
anonymous
  • anonymous
So in the case of the paper, cup it false because it was split up into two roots?
anonymous
  • anonymous
Yes. In case you still don't believe me ¬_¬ try putting in some numbers for r and h. sqrt(5^2 + 6^2) = sqrt(61) =/= 5 + 6
anonymous
  • anonymous
Oh, I believe you.
anonymous
  • anonymous
πr√(r^(2))+h^(2)=πr(√(r^(2))+√(h^(2)))=πr(r+h)

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