1
00:00:00,000 --> 00:00:00,800


2
00:00:00,800 --> 00:00:03,940
We're told that the radius of a sphere can be measured using

3
00:00:03,940 --> 00:00:08,759
the formula r is equal to the cube root of 3 times v,

4
00:00:08,759 --> 00:00:12,969
divided by 4pi, where v is equal to the volume.

5
00:00:12,970 --> 00:00:13,660
That's interesting.

6
00:00:13,660 --> 00:00:15,759
Normally you have it expressed the other way, volume as a

7
00:00:15,759 --> 00:00:17,230
function of radius.

8
00:00:17,230 --> 00:00:20,120
Here they have radius as a function of volume.

9
00:00:20,120 --> 00:00:23,679
If the radius of a sphere is 6 inches-- so they're giving us

10
00:00:23,679 --> 00:00:25,730
the radius; they're saying it's 6 inches.

11
00:00:25,730 --> 00:00:27,010
So they're giving us that right

12
00:00:27,010 --> 00:00:29,460
there-- what is its volume?

13
00:00:29,460 --> 00:00:33,179
So we have 6 inches-- everything's in inches-- is

14
00:00:33,179 --> 00:00:40,820
equal to the cube root of 3 times the volume-- that's what

15
00:00:40,820 --> 00:00:44,000
we need to solve for-- divided by 4pi.

16
00:00:44,000 --> 00:00:47,240
A good first step to get rid of this cube root, is take the

17
00:00:47,240 --> 00:00:50,620
cube of both sides or raise both sides of this equation to

18
00:00:50,619 --> 00:00:51,820
the third power.

19
00:00:51,820 --> 00:00:54,630
Let's see, it's 6 inches, you raise it to the third power.

20
00:00:54,630 --> 00:00:56,850
You have the cube root of 3v over 4pi.

21
00:00:56,850 --> 00:00:58,810
Raise it to the third power.

22
00:00:58,810 --> 00:01:01,830
And so the left-hand side of this equation becomes what?

23
00:01:01,829 --> 00:01:04,200
6 times 6 is 36.

24
00:01:04,200 --> 00:01:10,609
36 times 6 is 180, plus 36 is 216.

25
00:01:10,609 --> 00:01:12,620
So you have 216.

26
00:01:12,620 --> 00:01:14,603
And you had 6 inches here-- now that you're cubing it, it

27
00:01:14,602 --> 00:01:17,769
would actually now become 216 cubic inches, or inches

28
00:01:17,769 --> 00:01:24,629
cubed-- is equal to-- if you take the 3v divided by 4pi,

29
00:01:24,629 --> 00:01:26,479
the cube root is essentially taking it to the 1/3 power.

30
00:01:26,480 --> 00:01:27,719
Then take that to the third power.

31
00:01:27,719 --> 00:01:29,260
They unwind each other.

32
00:01:29,260 --> 00:01:33,600
So this just becomes 3v over 4pi.

33
00:01:33,599 --> 00:01:36,669
Now, to solve for volume, we can just multiply both sides

34
00:01:36,670 --> 00:01:41,500
of this equation times the inverse of its coefficient,

35
00:01:41,500 --> 00:01:44,659
times 4pi over 3.

36
00:01:44,659 --> 00:01:49,840
Times-- let me scroll to the leftt-- times 4pi over 3.

37
00:01:49,840 --> 00:01:52,159
Let me make sure you can see what I'm writing.

38
00:01:52,159 --> 00:01:54,239
And the whole reason why I'm multiplying by 4pi over 3 is

39
00:01:54,239 --> 00:01:56,959
so that it cancels out with the 3 over 4pi.

40
00:01:56,959 --> 00:02:00,699
And you have your 4pi cancels out with a 4pi, and then you

41
00:02:00,700 --> 00:02:03,329
have your 3 canceling out with a 3.

42
00:02:03,329 --> 00:02:08,159
And then you have, your volume is going to be equal to 4pi

43
00:02:08,159 --> 00:02:11,629
times 216 over 3.

44
00:02:11,629 --> 00:02:13,049
We could write it this way.

45
00:02:13,050 --> 00:02:24,070
216 times 4pi over 3.

46
00:02:24,069 --> 00:02:25,349
And we could simplify this.

47
00:02:25,349 --> 00:02:29,359
216, the digits add up to-- 2 plus 1, plus 6 is 9.

48
00:02:29,360 --> 00:02:30,610
So it will be divisible by 3.

49
00:02:30,610 --> 00:02:32,880
That's a fast way to test whether something's

50
00:02:32,879 --> 00:02:34,349
divisible by 3.

51
00:02:34,349 --> 00:02:35,449
So let's see what it is.

52
00:02:35,449 --> 00:02:39,239
3 goes into 216.

53
00:02:39,240 --> 00:02:41,110
3 goes into 21 seven times.

54
00:02:41,110 --> 00:02:43,290
7 times 3 is 21.

55
00:02:43,289 --> 00:02:44,370
Bring down the 6.

56
00:02:44,370 --> 00:02:45,890
You have no remainder, so bring down the 6.

57
00:02:45,889 --> 00:02:48,259
3 goes into 6 two times.

58
00:02:48,259 --> 00:02:50,069
2 times 3 is 6.

59
00:02:50,069 --> 00:02:52,299
No remainder, so it's 72.

60
00:02:52,300 --> 00:02:54,950
So 216 divided by 3 is 72.

61
00:02:54,949 --> 00:02:58,209
So it's 72 times 4pi is equal to the volume.

62
00:02:58,210 --> 00:03:00,120
It's going to be cubic inches.

63
00:03:00,120 --> 00:03:02,689
So 4 times 72.

64
00:03:02,689 --> 00:03:07,139
4 times 70 is 280.

65
00:03:07,139 --> 00:03:09,429
And then you have 4 times 2, which is 8.

66
00:03:09,430 --> 00:03:14,170
So it'll be 288pi cubic inches.

67
00:03:14,169 --> 00:03:16,869
That's our volume.

68
00:03:16,870 --> 00:03:18,460
And we're done.

69
00:03:18,460 --> 00:03:18,933