## anonymous 5 years ago if the volume of a sphere above is 4,500 π cubic units , what is the radius of the sphere A.) 15units B.)60units C.)5units D.)30units

1. anonymous

katie, lets do this together.

2. anonymous

okay :)

3. anonymous

do you know the formula for the volume of a sphere with radius r ?

4. anonymous

Ummm no i don't sorry

5. anonymous

okay. volume of a sphere is http://3.bp.blogspot.com/_z4R-m-_YJkA/Spd0j2ViRhI/AAAAAAAAAPg/70q7xqDA384/s320/volume-of-a-sphere.gif

6. anonymous

do i click on the link?

7. anonymous

yes.

8. anonymous

okay i got it. Thanks so thats step one

9. anonymous

okay great. so 4/3 pi r^3 = 4500 pi

10. anonymous

okay yes :)

11. anonymous

so solve for r.

12. anonymous

do i times a 4500 times 3?

13. anonymous

yes.

14. anonymous

and then?

15. anonymous

okay i got 13500 :)

16. anonymous

what does 13500 equal to?

17. anonymous

15 units

18. anonymous

huh?

19. anonymous

sorry i get the first part but i don't know what you mean whats it equal to

20. anonymous

okay lets start over. $4/3 * \pi * r ^{3} = 4500 \pi$

21. anonymous

okay

22. anonymous

so, $r ^{3} = 4500 \pi / (\pi*4/3) = 4500*3/4$

23. anonymous

okay which is 3375 right?

24. anonymous

yes

25. anonymous

26. anonymous

3?

27. anonymous

how did you get that?

28. anonymous

i looke at the formula

29. anonymous

okay and?

30. anonymous

31. anonymous

no. $r ^{3} = 3375 \rightarrow r = ?$

32. anonymous

if x^3 is 8, what is x?

33. anonymous

8x3=24 so 24

34. anonymous

okay x^3 means x cubed or x raised to the power 3. x is 2. 2 cube is 8. 2 raised to the power 3 is 8. In other words, 2 multiplied by itself 2 times is 8. i.e 8 = 2 times 2 times 2

35. anonymous

sorry multiplied by itself 3 times.

36. anonymous

2 is called the cube-root of 8.

37. anonymous

similarly radius cubed is 3375. so radius is cube root of 3375.

38. anonymous

39. anonymous

okay which is 7425

40. anonymous

do you know what square root is?

41. anonymous

yes hold on :0

42. anonymous

okay 61.4410

43. anonymous

what is 61.441 ?

44. anonymous

the square root

45. anonymous

of?

46. anonymous

3375

47. anonymous

sqrt(3 375) = 58.0947502

48. anonymous

I was asking you if you know the concept of square root.

49. anonymous

ohhh so the answer is b 60 units

50. anonymous

NO. pay attention.

51. anonymous

leave the problem for a moment. Do you know the concept of square root?

52. anonymous

i guess not..

53. anonymous

okay. if you multiply a number by itself. it will give you another number. For example, if you multiply 4 by itself, that is, multiply 4 by 4, you get 16.

54. anonymous

16 is the square of 4.

55. anonymous

okay

56. anonymous

and 4 is the square root of 16.

57. anonymous

do you know the area of a square?

58. anonymous

idk

59. anonymous

area of a square of side A is A*A. that is why this is called square and square root. anyway, thats not important,

60. anonymous

similarly, if you multiply a number by itself 3 times, you get another number. so if you multiply 4 by itself thrice, that is 4 times 4 times 4, you get 64.

61. anonymous

64 is the cube of 4. conversely, 4 is the cube root of 64.

62. anonymous

okay

63. anonymous

64. anonymous

so, to get radius, we need to find the cube root of 3375.

65. anonymous

okay

66. anonymous

now, 10*10*10 = 1000

67. anonymous

and 20*20*20 = 8000

68. anonymous

right?

69. anonymous

yes

70. anonymous

so r*r*r = 3375. 3375 lies between 1000 and 8000. so r must lie between 10 and 20. So, r is 15 units.

71. anonymous

ohhhhhh okay thank you so much :)

72. anonymous

you are welcome.