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anonymous
 5 years ago
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?
anonymous
 5 years ago
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?

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0x^3  still dont know the formula for a Sphere volume = free volume

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.04pir^3  ?? sounds familiar 3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I have 4/3 pi r^3 as the sphere volume

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I don't understand sphere volume = free volume

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0r = 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
 5 years ago
Best ResponseYou've already chosen the best response.0x^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
 5 years ago
Best ResponseYou've already chosen the best response.0What is the box volume to minus the sphere volume?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0suppose 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
 5 years ago
Best ResponseYou've already chosen the best response.0o.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
 5 years ago
Best ResponseYou've already chosen the best response.0that is correct: the volume of a square cubical box is: side times side times side...or side^3; lets call it x^3 :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the radius of the sphere is x/2 so my initial figureing was misappropriated.....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0am I suppose to subtract something?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how do I input the information into my calculator?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0do 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
 5 years ago
Best ResponseYou've already chosen the best response.0if 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
 5 years ago
Best ResponseYou've already chosen the best response.0The problem is how it's stated no numbers.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the length,width,and height of the box are equal to the diameter of the ball

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.024x^3  4pi(x^3)  x100 = percent free 24x^3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I don't understand how you got your numbers

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the volume of a box is (8x^3) 2x * 2x * 2x = 8x^3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I need the percent to the nearest tenth of a volume of the box not occupied by the ball

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0do 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
 5 years ago
Best ResponseYou've already chosen the best response.0Nope,the illustration only displays a ball inside of a cubicle box

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0then 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?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0I beleive I was up to here in the process then :) 24x^3  4pi(x^3)  x100 = percent free 24x^3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'm just having a difficult time with the process.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0I know.... but what we are doing is just substituting letter for number and working it thru.....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lets 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
 5 years ago
Best ResponseYou've already chosen the best response.0So,if I were to input your equation into my calculator I got the answer: 13823.9091

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i havent checked my own propensity for error yet :) lets get to the end of the process first ok?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0volume of box = 8x^3 volume of sphere = 4pi(x^3)  right? 3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(3)8x^3 4pi(x^3) 24(x^3)  4pi(x^3)    =  3 3 3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0which 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
 5 years ago
Best ResponseYou've already chosen the best response.0is this the simplest,straightforward method?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(6pi)  = 1  pi/6 this is a decimal value 6 we multiply it by 100 to get a number for the % 100(1pi/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 :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.047.64 % is the result I get :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Wow! So why do we have the equations over 3?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0becasue 100pi/6 reduces to 50pi/3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we could stop at: 100(1(pi/6)) and get the same results i spose :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hmm...I really need to look over the whole thing and digest this.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0you 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
 5 years ago
Best ResponseYou've already chosen the best response.0O.k. well,thank you for your trouble and time.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0....post a new question so I aint gotta scroll :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Write the trigonometric expression in terms of sine and cosine, and then simplify. sec(x)/csc(x)
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