## anonymous 5 years ago 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)

1. anonymous

Nonono. In general $\sqrt{a + b}\ \not= \sqrt{a} + \sqrt{b}$

2. anonymous

Could you explain your answer to me Mr. Newton?

3. anonymous

That simplification uses the assumption I listed above (splitting it up into two roots) The assumption is false.

4. anonymous

Hmmm

5. anonymous

It probably got confused with $\sqrt{a\times b} = \sqrt{a} \times \sqrt{b}$ which is true.

6. anonymous

So in the case of the paper, cup it false because it was split up into two roots?

7. 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

8. anonymous

Oh, I believe you.

9. anonymous

πr√(r^(2))+h^(2)=πr(√(r^(2))+√(h^(2)))=πr(r+h)