## anonymous one year ago *Area of the base equals* a)8 pi square units b)16 pi square units c) 64 pi square units

1. anonymous
2. anonymous

3. anonymous

@elic2k15

4. anonymous

@UsukiDoll

5. anonymous

@math1234

6. UsukiDoll

I'm juggling one question back in forth.. so if I'm slow to reply sorry in advanced. Anyway we are given a cylinder |dw:1435669876398:dw|

7. anonymous

It's okay

8. UsukiDoll

the formula for area of the base of a cylinder is A = pi(r^2)

9. anonymous

Okay. But every time I put it into the calculator it shows: either 39.4384 or 50.24

10. UsukiDoll

I know.. we don't calculate the pi part.. leave it as is. so if r = 4 what is r^2?

11. UsukiDoll

looking at the choices... I think it doesn't want you to calculate the pi.. it's just finding the r and then squaring it

12. anonymous

Well then it's just 16

13. anonymous

So it's B?

14. UsukiDoll

A=pi(4^2) A=pi(16) =16 pi yeah

15. anonymous

Thanks. So would it be about the same thing for this problem?

16. anonymous

A cylinder has a volume of 245 pi cubic units and a height of 5 units. The diameter of the cylinder is a) 7 units b) 14 units c) 49 units

17. UsukiDoll

I think we need the diameter of the cylinder formula.

18. UsukiDoll

yeah we need a different formula for that.

19. UsukiDoll

$\large V = \pi r^2h$

20. UsukiDoll

so given height is 5 units volume is 245 pi cubic units . Looks like we're solve for r and then the diameter is twice the radius (d=2r) .. AHA! We need to find the radius first

21. anonymous

Yes

22. UsukiDoll

ok let V = 245, and h = 5

23. anonymous

V r h = � or 2 =

24. anonymous

Well that didn't come out right

25. anonymous

:(

26. UsukiDoll

$\large 245 = \pi r^2(5)$

27. anonymous

What's "large"?

28. UsukiDoll

that's to make the font large

29. UsukiDoll

oh are you trying to use the equation tool? right click show math as -> tex command and it will have this code or text you can copy and paste. And then click on the equation tool and paste.

30. anonymous

Oh

31. UsukiDoll

so we are solving for r that would mean that r needs to be by itself

32. UsukiDoll

our first goal is to have r^2 by itself .. and then afterwards we can take the square root

33. anonymous

$V = \pi r2h$

34. anonymous

r is squared

35. UsukiDoll

yeah it should have that ^ that carrot sign

36. UsukiDoll

$\large V = \pi r^2h$

37. UsukiDoll

anyway back to this $\large 245 = \pi r^2(5)$ we need r^2 by itself so what do we need to do?

38. UsukiDoll

should we add both sides? subtract both sides? multiply both sides? or.. divide both sides by 5pi

39. anonymous

divide both sides by 5 pi

40. UsukiDoll

yes. $\large \frac{245}{5 \pi} = r^2$

41. UsukiDoll

now we take the square root of both sides

42. anonymous

So 49 = ?

43. anonymous

Umm

44. UsukiDoll

we're not done.. we need to take the square root on both sides

45. UsukiDoll

UH OH! I need to refresh my screen is crazy

46. anonymous

kk

47. anonymous

48. anonymous

I neded to digest a little

49. UsukiDoll

ok so taking the square root of both sides $\large \sqrt{ \frac{245}{5 \pi} }= \sqrt{r^2}$ what is the square root of r^2

50. UsukiDoll

we need to take the square root of r^2 so we can have r

51. UsukiDoll

then once we have our r we can get the diameter. which is d =2r

52. anonymous

r=2.5

53. UsukiDoll

that's not a choice for answers that would've yielded d = 5.. that's not right

54. anonymous

No wait. 5 was the height not the diameter

55. anonymous

56. UsukiDoll

wait a minute we are solving for r.

57. UsukiDoll

we have already plugged in V and h... now we need to take the square root of both sides. We're almost there

58. anonymous

I was thinking that the diameter is 7

59. anonymous

cus 7 squared is 49

60. UsukiDoll

$\large \sqrt{ \frac{245}{5 \pi} }= \sqrt{r^2}$ becomes ??? what is the square root of r^2

61. anonymous

49 times 3.14 = 153.86

62. anonymous

Umm

63. anonymous

7

64. UsukiDoll

once we find r we can find the diameter which is d = 2r

65. UsukiDoll

What? ok no substituting we are solving for r we need the square root of r^2 .

66. UsukiDoll

I want an r by itself

67. UsukiDoll

we have square rooted both sides.. which is correct. Now we just need the square root of r^2 Then we have this $\[\[\large \sqrt{ \frac{245}{5 \pi} }= r$ \]

68. UsukiDoll

now the diameter is d=2r so d = 2( That whole square root)

69. UsukiDoll

$\large \sqrt{r^2} \rightarrow r^{\frac{2}{2}} \rightarrow r^1 \rightarrow r$

70. UsukiDoll

so now our $d=2(\sqrt{\frac{245}{5 \pi}})$

71. UsukiDoll

so we just need 245 divided by 5 pi... take the square root of that result and multiply by 2

72. anonymous

7.9

73. UsukiDoll

yes. so our diameter is 7.9 kind of a dangerous number because we can round up to 8

74. UsukiDoll

7 units would be the closest to the answer.. though the real answer is 7.9

75. anonymous

Okay. Look I'm sorry if I aggravated you. It's been a long couple of weeks and I'm really tired

76. anonymous

Thanks for the help. I really appreciate it

77. UsukiDoll

it's ok ... I'm also tired.. in fact it's almost 4 in the morning. I need zzz's before my dad get suspicious again.

78. UsukiDoll

that's why I had my latex wrong... r to the first power is just r if it was r^0 that would've been 1. But I should always take the advice of never do math while tired.

79. anonymous

Yeah I can connect with that

80. UsukiDoll

I have to go sleep. night

81. anonymous

Really. Wow it's 9:55 AM here

82. anonymous

well alright

83. anonymous

I live in Florida btw