Question

a golf ball is packed into a cubical box so that it just fits. what percentage of the box is unfilled?

Answer 1

volume of box - volume of ball

Answer 2

divide by volume of box

Answer 3

That is what I did. Isn't the 2x radius the same as length, width, height of the cubic box?

Answer 4

foe a cube length=breadth=height=l
volume=l^3
volume of ball=4/3*pi*r^3

Answer 5

My answer is 476.4%

Answer 6

Is that how we do it?

Answer 7

(l^3-4/3*pi*r^3)/l^3

Answer 8

ans will be less than 100%

Answer 9

You'll get a different answer (0.869)

Answer 10

numerator will be less then denominator
let ans is 0.99999
for % calculation
0.99999*100=99.999
so it can not go above 100

give me the value i will solve fr u

Answer 11

They haven't given a value but one can conclude that if the radius is 5 then the height, length and width are all equal to 10 as the golf ball perfectly fits the cubic box

Answer 12

You would need to draw it

Answer 13

to find the percentage of the box that is unfilled you can just find the percentage of the box that is filled and subtract that from 100%

Answer 14

to find this, you can assume the radius of the sphere to be 1, which makes the side length of the box 2, your reasoning above is correct.

Answer 15

area of a cube = side^3 = 8
area of a sphere = 4/3 pi*r^3 = 4/3 pi

Answer 16

so the percent filled is \[\frac {\frac{ 4 }{ 3 }\times \pi}{8}\]

Answer 17

and from there you can find the percent empty @Chad123 you see how this works?

Answer 18

@Peter14
we have to calculate empty space ratio so
(8-4*pi/3)/8

Answer 19

Thanks guys

Answer 20

yes, @gorv I specified earlier that you subtract the percent filled space from 100

Answer 21

So we don't have to convert the answer into a %?

Answer 22

@Peter14
actually i didn't see that sorry for that