helpppp:(

Two identical solid spheres fit exactly inside a cuboid box. Find the percentage of the volume of the box which is occupied by the spheres. Give your answer to 1dp.
I've already figured out the formula for surface area of a sphere (4/3pie r^2) and I know the height would be 4r and the base 2r (diameter), although I'm unsure of what to do from here.
ANY HELP WOULD BE APPRECIATED

Aren't you supposed to work out the volume of each sphere rather than the surface area?
(And another thing I'd do would be to somehow relate measurements on the spheres to the width, length and height of the cuboid.)

I meant volume rather than surface area, sorry but from there I'm not sure what to do, as I have related the lengths of the cuboid in terms of the radius of the sphere. Could you guide me as to what to do after this?
The height would be 4 x radius (4r) and the base 2r (2 x radius)

Don't forget that since the sphere is a 3D shape, the width would also be 2r. Using these measurements you have for the cuboid, you should then have a value for the volume in terms of r.

So the volume of the cuboid would be 16r^3 because 2r x 4r x 2r
Then the volume of the two spheres would be 8/3 x pie^2 x r^4
I don't understand what's next, as r is an unknown value...

Well, since finding the percentage is the same as dividing one value by another and then multiplying by 100, you could make a fraction from the volume for the two spheres and the volume of the cuboid.

If you think about it, however much you scale the box & spheres, the ratio of sphere volume to box volume is never going to change. Double it, you double both volumes, so the percentage is the same.

This means it's going to cancel out. The volume of the spheres will be some multiple of r cubed, and the volume of the spheres should be some multiple of r cubed. r cubed/r cubed = 1, so it's just the ratio of the multiples.

It's also exactly the same as one sphere in a box, as the two "sides" of the box are identical, so have the same ratio.

But wouldn't the volume of the spheres together be r^4 because r^2 x r^2

Actually, it wouldn't be - you're adding the two volumes together to get the total volume of the spheres.

Ohh, I just realised I have been writing the formula wrong the whole time:' )
So would the equation be...
16r^3/ (8/3 x 2pie x 2r^2)?

checked on a calculator, you're right with that answer, i screwed the arithmetic up. question wants 1dp though

Actually, it wouldn't be - you're adding the two volumes together to get the total volume of the spheres.

Has anyone got a final answer for this ?