A spherical bar of soap just fits inside its package, which is a cube with a side length of 8cm.
a)what is the volume of the bar of soap?
b)calculate the amount of empty space in the box.

Question

anonymous · Answer

I think its b
But remember, I am 99% falling a sleep

shelby1290 · Answer

@Dark_Riddles lol it's not a multiple choice question

kainui · Answer

Draw a picture @shelby1290 and try to label it. 

Do you know what the formula for volume of a sphere and cube are?

anonymous · Answer

Oh my god
Been doing this math all wrong then xD

shelby1290 · Answer

@Dark_Riddles LOL 
@Kainui alright

shelby1290 · Answer

the best i can do

shelby1290 · Answer

|dw:1401871182716:dw|

kainui · Answer

Maybe this will be better to get the point across: |dw:1401871179104:dw| There, it doesn't look 3D what I did but now it's easier to see the relationships. Can you label anything on the circle and cube that you can use to find their volumes?

shelby1290 · Answer

i'd say you have to shade the corners of the square

kainui · Answer

Well, you can if you like, but it's really not that important. Do you know the formulas for volume of sphere and cube?

shelby1290 · Answer

sphere: V=(4/3)pi x r^3

shelby1290 · Answer

cube:V=a^3

shelby1290 · Answer

or s^3

kainui · Answer

Yeah, all good. So now that you have this info can you use it along with the picture to determine part a) of your question?

kainui · Answer

Try your best, I'll help you figure it out if you get stuck.

shelby1290 · Answer

cube=8^3 = 512cm^3

shelby1290 · Answer

@Kainui i don't know what to do next

shelby1290 · Answer

for the sphere

kainui · Answer

So what do you need to find the volume of the bar of soap? What's stopping you from solving that equation? Can you use the picture to find that number? |dw:1401871671370:dw|

shelby1290 · Answer

i think you divide 8 by 2 to get 4 
so the radius becomes 4cm

kainui · Answer

Yeah now we're thinking. =)

shelby1290 · Answer

and then you substitute everything into the equation and get 268cm^3

kainui · Answer

Wait, remember the bar of soap is a sphere so its volume is:

V=(4/3)pi x r^3

and you said the radius was 4cm.

shelby1290 · Answer

yea i got 268

shelby1290 · Answer

to find the empty space do i subtract the area of the sphere and the area of the cube from eachother?

kainui · Answer

Yeah exactly. That's it. Sorry I didn't realize you had rounded.

shelby1290 · Answer

np and i got 244cm^3 for the amount of empty space left

shelby1290 · Answer

am i right/

kainui · Answer

Yeah, that sounds about right to me. Good job. =)