anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
katie, lets do this together.
anonymous
  • anonymous
okay :)
anonymous
  • anonymous
do you know the formula for the volume of a sphere with radius r ?

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anonymous
  • anonymous
Ummm no i don't sorry
anonymous
  • 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
  • anonymous
do i click on the link?
anonymous
  • anonymous
yes.
anonymous
  • anonymous
okay i got it. Thanks so thats step one
anonymous
  • anonymous
okay great. so 4/3 pi r^3 = 4500 pi
anonymous
  • anonymous
okay yes :)
anonymous
  • anonymous
so solve for r.
anonymous
  • anonymous
do i times a 4500 times 3?
anonymous
  • anonymous
yes.
anonymous
  • anonymous
and then?
anonymous
  • anonymous
okay i got 13500 :)
anonymous
  • anonymous
what does 13500 equal to?
anonymous
  • anonymous
15 units
anonymous
  • anonymous
huh?
anonymous
  • anonymous
sorry i get the first part but i don't know what you mean whats it equal to
anonymous
  • anonymous
okay lets start over. \[4/3 * \pi * r ^{3} = 4500 \pi\]
anonymous
  • anonymous
okay
anonymous
  • anonymous
so, \[r ^{3} = 4500 \pi / (\pi*4/3) = 4500*3/4 \]
anonymous
  • anonymous
okay which is 3375 right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
and so the radius is?
anonymous
  • anonymous
3?
anonymous
  • anonymous
how did you get that?
anonymous
  • anonymous
i looke at the formula
anonymous
  • anonymous
okay and?
anonymous
  • anonymous
idk is the radus 3375
anonymous
  • anonymous
no. \[r ^{3} = 3375 \rightarrow r = ?\]
anonymous
  • anonymous
if x^3 is 8, what is x?
anonymous
  • anonymous
8x3=24 so 24
anonymous
  • 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
  • anonymous
sorry multiplied by itself 3 times.
anonymous
  • anonymous
2 is called the cube-root of 8.
anonymous
  • anonymous
similarly radius cubed is 3375. so radius is cube root of 3375.
anonymous
  • anonymous
use your calculator to find the cube root of 3375. that is your radius.
anonymous
  • anonymous
okay which is 7425
anonymous
  • anonymous
do you know what square root is?
anonymous
  • anonymous
yes hold on :0
anonymous
  • anonymous
okay 61.4410
anonymous
  • anonymous
what is 61.441 ?
anonymous
  • anonymous
the square root
anonymous
  • anonymous
of?
anonymous
  • anonymous
3375
anonymous
  • anonymous
sqrt(3 375) = 58.0947502
anonymous
  • anonymous
I was asking you if you know the concept of square root.
anonymous
  • anonymous
ohhh so the answer is b 60 units
anonymous
  • anonymous
NO. pay attention.
anonymous
  • anonymous
leave the problem for a moment. Do you know the concept of square root?
anonymous
  • anonymous
i guess not..
anonymous
  • 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
  • anonymous
16 is the square of 4.
anonymous
  • anonymous
okay
anonymous
  • anonymous
and 4 is the square root of 16.
anonymous
  • anonymous
do you know the area of a square?
anonymous
  • anonymous
idk
anonymous
  • 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
  • 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
  • anonymous
64 is the cube of 4. conversely, 4 is the cube root of 64.
anonymous
  • anonymous
okay
anonymous
  • anonymous
okay so, if the radius is multiplied by itself 3 times, you get 3375. so, radius*radius*radius = 3375
anonymous
  • anonymous
so, to get radius, we need to find the cube root of 3375.
anonymous
  • anonymous
okay
anonymous
  • anonymous
now, 10*10*10 = 1000
anonymous
  • anonymous
and 20*20*20 = 8000
anonymous
  • anonymous
right?
anonymous
  • anonymous
yes
anonymous
  • 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
  • anonymous
ohhhhhh okay thank you so much :)
anonymous
  • anonymous
you are welcome.

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