anonymous
  • anonymous
A figure shows a cubical box with a sphere that just fits inside.That is,the length,width,and height of the box are each equal to the diameter of the ball.What percent to the nearest tenth of the volume of the box is not occupied by the ball?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
lol again?
amistre64
  • amistre64
x^3 - still dont know the formula for a Sphere volume = free volume
amistre64
  • amistre64
4pir^3 ------ ?? sounds familiar 3

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anonymous
  • anonymous
I have 4/3 pi r^3 as the sphere volume
anonymous
  • anonymous
I don't understand sphere volume = free volume
amistre64
  • amistre64
r = x so lets run with that. it means that the sphere eats up so much of the boxes volume that whatever is not taken up by the sphere is "free"....empty space
amistre64
  • amistre64
x^3 - 4pi(x^3) ------- 3 3x^3 - 4pi(x^3) -------------- 3 x^3(3 - 4pi) ---------- should be the free space in the box. 3
anonymous
  • anonymous
What is the box volume to minus the sphere volume?
amistre64
  • amistre64
suppose you have a bathtub filled with bubble bath till lits almost overflowing.... when you get in, the volume of water that flows out is taken up by the volume of your body getting in; when you get out of the tub, the amount of water left in is the stuff that didnt overflow to begin with and it is equal to: volume of tub - volume of you...
anonymous
  • anonymous
o.k. I can imagine that,but in order for me to resolve this problem I need the formula of the volume for the box and sphere.
amistre64
  • amistre64
that is correct: the volume of a square cubical box is: side times side times side...or side^3; lets call it x^3 :)
amistre64
  • amistre64
the radius of the sphere is x/2 so my initial figureing was misappropriated.....
anonymous
  • anonymous
am I suppose to subtract something?
anonymous
  • anonymous
how do I input the information into my calculator?
anonymous
  • anonymous
What is the percent?
amistre64
  • amistre64
do you have a "real" value for the sides of the box? or the radius of the sphere? without that, you are left with a formula with variables in it
amistre64
  • amistre64
if we assume the box side is twice the radius of the sphere; we get: 4pi(x^3) 8x^3 - ------- for the free volume in the box 3
anonymous
  • anonymous
The problem is how it's stated -no numbers.
anonymous
  • anonymous
the length,width,and height of the box are equal to the diameter of the ball
amistre64
  • amistre64
24x^3 - 4pi(x^3) ---------------- x100 = percent free 24x^3
anonymous
  • anonymous
I don't understand how you got your numbers
amistre64
  • amistre64
the volume of a box is (8x^3) 2x * 2x * 2x = 8x^3
anonymous
  • anonymous
I need the percent to the nearest tenth of a volume of the box not occupied by the ball
amistre64
  • amistre64
do you agree that the volume of the box is 8x^3? if there is a figure that goes with the question....tell me, does it show a number for the raduis of the sphere or perhaps a number for the side of the box?
anonymous
  • anonymous
Nope,the illustration only displays a ball inside of a cubicle box
amistre64
  • amistre64
then we will have to see if our variables cancel out at some point in the process........ when we get to the end of the process, lets see if we get a "percentage" that doesnt include a variable then.... you agree?
anonymous
  • anonymous
Yes,agree.
amistre64
  • amistre64
I beleive I was up to here in the process then :) 24x^3 - 4pi(x^3) ---------------- x100 = percent free 24x^3
anonymous
  • anonymous
I'm just having a difficult time with the process.
amistre64
  • amistre64
I know.... but what we are doing is just substituting letter for number and working it thru.....
amistre64
  • amistre64
lets say the radius of the sphere is equal to "x" the radius of the sphere is exactly "half" the measurement of a side of the box; so 2x = the width, the height and the depth of the box. w*h*d = 2x * 2x * 2x = 8x^3 you agree?
anonymous
  • anonymous
So,if I were to input your equation into my calculator I got the answer: 13823.9091
amistre64
  • amistre64
i havent checked my own propensity for error yet :) lets get to the end of the process first ok?
amistre64
  • amistre64
volume of box = 8x^3 volume of sphere = 4pi(x^3) -------- right? 3
anonymous
  • anonymous
o.k. then what?
amistre64
  • amistre64
(3)8x^3 4pi(x^3) 24(x^3) - 4pi(x^3) ------- - ------- = ---------------- 3 3 3
amistre64
  • amistre64
which equals: 4x^3(6 - pi) ---------- 3 we divide this "value" by the volume of the box: 8x^3 4x^3(6 - pi) ---------- / 8x^3 3 4x^3(6 - pi) ---------- we can cancel out like terms and reduce this. 24x^3
anonymous
  • anonymous
is this the simplest,straightforward method?
amistre64
  • amistre64
(6-pi) ----- = 1 - pi/6 this is a decimal value 6 we multiply it by 100 to get a number for the % 100(1-pi/6) = 100 - 50pi/3. the calculator says .........its the simplest and straight forward answer yes; do you really think Id waste my time helping you for a joke?.....dont interupt :)
anonymous
  • anonymous
:) sorry.
amistre64
  • amistre64
47.64 % is the result I get :)
anonymous
  • anonymous
Wow! So why do we have the equations over 3?
amistre64
  • amistre64
becasue 100pi/6 reduces to 50pi/3
amistre64
  • amistre64
we could stop at: 100(1-(pi/6)) and get the same results i spose :)
anonymous
  • anonymous
Hmm...I really need to look over the whole thing and digest this.
amistre64
  • amistre64
you do that..... and since the "x" variable vanishes in the end, we probably could have went with a value of x=1 to begin with; but i wasnt sure if it was going to work out that well :)
anonymous
  • anonymous
O.k. well,thank you for your trouble and time.
amistre64
  • amistre64
youre welcome :)
anonymous
  • anonymous
oh.... amistre :)
amistre64
  • amistre64
....yes???
anonymous
  • anonymous
help please <3
amistre64
  • amistre64
....post a new question so I aint gotta scroll :)
anonymous
  • anonymous
ok
anonymous
  • anonymous
Write the trigonometric expression in terms of sine and cosine, and then simplify. sec(x)/csc(x)

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