Question

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?

Answer 1

lol again?

Answer 2

x^3 - still dont know the formula for a Sphere volume = free volume

Answer 3

4pir^3
------ ?? sounds familiar
3

Answer 4

I have 4/3 pi r^3 as the sphere volume

Answer 5

I don't understand sphere volume = free volume

Answer 6

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

Answer 7

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

Answer 8

What is the box volume to minus the sphere volume?

Answer 9

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...

Answer 10

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.

Answer 11

that is correct:

the volume of a square cubical box is:

side times side times side...or side^3; lets call it x^3 :)

Answer 12

the radius of the sphere is x/2 so my initial figureing was misappropriated.....

Answer 13

am I suppose to subtract something?

Answer 14

how do I input the information into my calculator?

Answer 15

What is the percent?

Answer 16

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

Answer 17

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

Answer 18

The problem is how it's stated -no numbers.

Answer 19

the length,width,and height of the box are equal to the diameter of the ball

Answer 20

24x^3 - 4pi(x^3)
---------------- x100 = percent free
24x^3

Answer 21

I don't understand how you got your numbers

Answer 22

the volume of a box is (8x^3)

2x * 2x * 2x = 8x^3

Answer 23

I need the percent to the nearest tenth of a volume of the box not occupied by the ball

Answer 24

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?

Answer 25

Nope,the illustration only displays a ball inside of a cubicle box

Answer 26

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?

Answer 27

Yes,agree.

Answer 28

I beleive I was up to here in the process then :)

24x^3 - 4pi(x^3)
---------------- x100 = percent free
24x^3

Answer 29

I'm just having a difficult time with the process.

Answer 30

I know.... but what we are doing is just substituting letter for number and working it thru.....

Answer 31

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?

Answer 32

So,if I were to input your equation into my calculator I got the answer: 13823.9091

Answer 33

i havent checked my own propensity for error yet :) lets get to the end of the process first ok?

Answer 34

volume of box = 8x^3

volume of sphere = 4pi(x^3)
-------- right?
3

Answer 35

o.k. then what?

Answer 36

(3)8x^3 4pi(x^3) 24(x^3) - 4pi(x^3)
------- - ------- = ----------------
3 3 3

Answer 37

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

Answer 38

is this the simplest,straightforward method?

Answer 39

(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 :)

Answer 40

:) sorry.

Answer 41

47.64 % is the result I get :)

Answer 42

Wow! So why do we have the equations over 3?

Answer 43

becasue 100pi/6 reduces to 50pi/3

Answer 44

we could stop at:
100(1-(pi/6)) and get the same results i spose :)

Answer 45

Hmm...I really need to look over the whole thing and digest this.

Answer 46

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 :)

Answer 47

O.k. well,thank you for your trouble and time.

Answer 48

youre welcome :)

Answer 49

oh.... amistre :)

Answer 50

....yes???

Answer 51

help please <3

Answer 52

....post a new question so I aint gotta scroll :)

Answer 53

ok

Answer 54

Write the trigonometric expression in terms of sine and cosine, and then simplify.

sec(x)/csc(x)