Question

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

Answer 1

katie, lets do this together.

Answer 2

okay :)

Answer 3

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

Answer 4

Ummm no i don't sorry

Answer 5

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

Answer 6

do i click on the link?

Answer 7

yes.

Answer 8

okay i got it. Thanks so thats step one

Answer 9

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

Answer 10

okay yes :)

Answer 11

so solve for r.

Answer 12

do i times a 4500 times 3?

Answer 13

yes.

Answer 14

and then?

Answer 15

okay i got 13500 :)

Answer 16

what does 13500 equal to?

Answer 17

15 units

Answer 18

huh?

Answer 19

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

Answer 20

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

Answer 21

okay

Answer 22

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

Answer 23

okay which is 3375 right?

Answer 24

yes

Answer 25

and so the radius is?

Answer 26

3?

Answer 27

how did you get that?

Answer 28

i looke at the formula

Answer 29

okay and?

Answer 30

idk is the radus 3375

Answer 31

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

Answer 32

if x^3 is 8, what is x?

Answer 33

8x3=24 so 24

Answer 34

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

Answer 35

sorry multiplied by itself 3 times.

Answer 36

2 is called the cube-root of 8.

Answer 37

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

Answer 38

use your calculator to find the cube root of 3375. that is your radius.

Answer 39

okay which is 7425

Answer 40

do you know what square root is?

Answer 41

yes hold on :0

Answer 42

okay 61.4410

Answer 43

what is 61.441 ?

Answer 44

the square root

Answer 45

of?

Answer 46

3375

Answer 47

sqrt(3 375) = 58.0947502

Answer 48

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

Answer 49

ohhh so the answer is b 60 units

Answer 50

NO. pay attention.

Answer 51

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

Answer 52

i guess not..

Answer 53

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.

Answer 54

16 is the square of 4.

Answer 55

okay

Answer 56

and 4 is the square root of 16.

Answer 57

do you know the area of a square?

Answer 58

idk

Answer 59

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

Answer 60

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.

Answer 61

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

Answer 62

okay

Answer 63

okay
so, if the radius is multiplied by itself 3 times, you get 3375.
so, radius*radius*radius = 3375

Answer 64

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

Answer 65

okay

Answer 66

now, 10*10*10 = 1000

Answer 67

and 20*20*20 = 8000

Answer 68

right?

Answer 69

yes

Answer 70

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

Answer 71

ohhhhhh okay thank you so much :)

Answer 72

you are welcome.