## anonymous one year ago a can of beans has surface area 359 cm^2. Its height is 10 cm. What is the radius of the circular top?

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1. anonymous

Do you know the formula for calculating the surface area of a sphere?

2. anonymous

2pir^2+2pirh?

3. anonymous

oh wait just pir^2?

4. anonymous

Pir^2 is just the surface area of one lid, so for the 2 lids it would be 2Pir^2 what is the formula for the walls?

5. anonymous

2pirh?

6. anonymous

7. anonymous

im following the steps the teacher gave me for notes but i keep getting them wrong. This is the 5th problem like this I've attempted to do.

8. anonymous

The wall of the can would be circumference x height. (The height is given). What is the circumference?

9. anonymous

I did not calculate the answer. I'm doing step by step with you.

10. anonymous

I apologize, you wrote the correct answer earlier. The surface area of the wall is 2 pirh.

11. anonymous

And what you wrote the very first time "2pir^2+2pirh" is also correct.

12. anonymous

359=2pir^2 + 20pir?

13. anonymous

So far looks good. It may be easier to factor out a 2 and write it as 359 = 2 (pir^2 + 10pir). You're on the right track.

14. anonymous

in my notes my teacher has me equal it out to 0 following this it would be 0 = 2pir^2+20pir-359

15. phi

this one is more painful than that. How about divide all term by 2pi and write it as $r^2 + 10 r - \frac{359}{2 \pi} = 0$ if we use a calculator, that is about $r^2 + 10 r - 57.1366=0$ to find r we could use the quadratic formula

16. anonymous

after that step i'm getting very confused

17. anonymous

Give me a few minutes. I'll try it the way you have it in your notes.

18. anonymous

x=-b+- sqr rt, b^2-4ac / 2a

19. anonymous

20. anonymous

okay thank you

21. phi

yes, quadratic formula. if you first divide by 2pi most of the numbers get a bit smaller and you would have a=1, b=10 , c= 57.1366

22. anonymous

-10pi+- sq rt. 100-4(!)(57.1366)/2?

23. phi

if you are doing $r^2 + 10 r - 57.1366=0$ -b is -10 (not -10pi) a=1 so 4ac is just 4*-57.1366 (notice c is negative)

24. phi

so $\frac{-10+ \sqrt{100 + 228.5465}}{2}$

25. phi

I would pick the + sqrt because otherwise we get a negative radius

26. anonymous

114.27325

27. anonymous

am i calculating this right

28. anonymous

i feel so wrong

29. phi

yes, not correct.

30. anonymous

what am i doing wronnggggg

31. phi

can you get this far: $\frac{-10+ \sqrt{100 + 228.5465}}{2}$ (by the way for c = -359/(2pi) I would use all the digits the calculator has)

32. anonymous

-28.56831228

33. phi

for $r^2 + 10 r - 57.1366=0$ a=1, b=10, c= -57.1366 (roughly) let's first figure out b^2 -4 * a *c that is 100 - 4 * 1 * -57.1366 what does that simplify to ?

34. anonymous

i'm getting -118.5465.

35. phi

4*-57.1366= -228.5465 now do 100 - (-228.5465)

36. anonymous

I made a mistake in my calculation. I don't want to post until I figure out where the error is.

37. phi

notice it is minus a minus. that makes it a +

38. anonymous

OHHHHHHH, 328.5465

39. anonymous

i forgot the other minus

40. phi

yes. so make a note: Be careful about the minus signs (they are evil) now find the square root.

41. anonymous

4.062925852??????

42. phi

yes, that looks good. do they want the answer rounded ?

43. anonymous

yes, 4.06

44. anonymous

so i was right earlier. Thank you both so much for your help!

45. anonymous

46. phi

if we use 4.06 in the original formula we get 358.67 or about 359, so it checks out.

47. anonymous

If it helps I'll post how to do it in a calculator that has fractions

48. anonymous

$\frac{ -20 + \sqrt{20^2+ 8(\frac{ 359 }{ \pi })} }{ 4 }$

49. anonymous

If your calculator allows you to enter the above equation (in one step) you'll get the same answer. I put in + 8 since the two negatives become positive.