SOLUTION: Hi there! I am not very good at math and I have been stuck on this question for 20 minutes now. The question is: calculate the volume of a box to hold a sphere-shaped beaker with a

Question 953226: Hi there! I am not very good at math and I have been stuck on this question for 20 minutes now. The question is: calculate the volume of a box to hold a sphere-shaped beaker with a volume of 413cm^3. The second part is : how much space is being occupied by the beaker and how much is being wasted, in percents.
Thank you so much, I honestly have no idea what to do.
Found 2 solutions by macston, josmiceli:
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
Volume of sphere=
Multiply each side by

Find the cube root of each side.
4.62cm=r
The cubic box to hold the sphere must have edges=2r (diameter of the sphere)
The volume of the cube ===
Volume of cube=789 cm^3
Volume wasted=vol(cube)-vol(sphere)=789cm^3-413cm^3=376cm^3
Percent of cube volume wasted=vol(wasted)/vol(cube)=(376cm^3/789cm^3)(100%)=47.7%
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The volume of a sphere is:

where is the radius
-----------------------
You are given that:
cm3
---------------------

Multiply both sides by

Divide both sides by

---------------
check:

This looks close enough
-----------------------
If this sphere is tightly enclosed in a cube,
the volume of the box is
This is because is equal to a side
of the box
-----------------

----------------------

( wasted volume in cm3 )
-------------------------
You are asked for:
which is a %

47.64% is wasted space inside the cube
----------------
Hope I got it -tough calculations

RELATED QUESTIONS
I have not really been to good at math and I never had a good Alg. teacher b/c they all... (answered by longjonsilver,richwmiller)
The question is , the lenght of a rectangle is twice the width. The area is 648sqrt. find (answered by stanbon)
Hello, I am a student who is in Grade 11 and in Mathematics Grade 11 Foundations. We... (answered by mouk)
Hi there! I have been stuck on this one logic problem for the longest time. I am a... (answered by jim_thompson5910)
I am having a difficult time with this question, its been 10 years since needing to do... (answered by solver91311)
I couldn't find the right category for my question. I'm working on conditional statements (answered by Edwin McCravy)
Hello good people. i was wondering if there were any person whom come tell me the answer... (answered by edjones)
I couldn't find the right category for my question. I'm working on conditional statements (answered by solver91311)
Ok, I am not very good at math and I need some help with this question. m/5=14 I am... (answered by jim_thompson5910)