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

- anonymous

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- anonymous

katie, lets do this together.

- anonymous

okay :)

- anonymous

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

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- anonymous

Ummm no i don't sorry

- anonymous

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

- anonymous

do i click on the link?

- anonymous

yes.

- anonymous

okay i got it. Thanks so thats step one

- anonymous

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

- anonymous

okay yes :)

- anonymous

so solve for r.

- anonymous

do i times a 4500 times 3?

- anonymous

yes.

- anonymous

and then?

- anonymous

okay i got 13500 :)

- anonymous

what does 13500 equal to?

- anonymous

15 units

- anonymous

huh?

- anonymous

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

- anonymous

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

- anonymous

okay

- anonymous

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

- anonymous

okay which is 3375 right?

- anonymous

yes

- anonymous

and so the radius is?

- anonymous

3?

- anonymous

how did you get that?

- anonymous

i looke at the formula

- anonymous

okay and?

- anonymous

idk is the radus 3375

- anonymous

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

- anonymous

if x^3 is 8, what is x?

- anonymous

8x3=24 so 24

- 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

- anonymous

sorry multiplied by itself 3 times.

- anonymous

2 is called the cube-root of 8.

- anonymous

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

- anonymous

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

- anonymous

okay which is 7425

- anonymous

do you know what square root is?

- anonymous

yes hold on :0

- anonymous

okay 61.4410

- anonymous

what is 61.441 ?

- anonymous

the square root

- anonymous

of?

- anonymous

3375

- anonymous

sqrt(3 375) = 58.0947502

- anonymous

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

- anonymous

ohhh so the answer is b 60 units

- anonymous

NO. pay attention.

- anonymous

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

- anonymous

i guess not..

- 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.

- anonymous

16 is the square of 4.

- anonymous

okay

- anonymous

and 4 is the square root of 16.

- anonymous

do you know the area of a square?

- anonymous

idk

- 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,

- 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.

- anonymous

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

- anonymous

okay

- anonymous

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

- anonymous

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

- anonymous

okay

- anonymous

now, 10*10*10 = 1000

- anonymous

and 20*20*20 = 8000

- anonymous

right?

- anonymous

yes

- 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.

- anonymous

ohhhhhh okay thank you so much :)

- anonymous

you are welcome.

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