Three mutually tangent spheres of radius 1 rest on a horizontal plane. A sphere of radius 2 rests on them. What is the distance from the plane to the top of the larger sphere?
4+sqrt((5+4sqrt(3))/3) = 5.994007959719612
That is what I get.
If you want me to justify that you will need to prompt me.
plus I am busy at present so you will probably have to wait a bit.
Maybe it is wrong but you are expected to say why you believe it to be so.
Maybe you are just a stupid brat who has recently learned how to spell 'wrong' and you are trying to impress the world with your great knowledge.
Considering that you have written 'wrong' as a response to a couple of answers very recently I expect my explanation of your motives sounds very likely.
no one has use for you in the world. you potatoes who cheat homework, but you end up failing the EASIEST thing to do. CHEAT!
You use our answers without any understanding on how we got it, then you blame us for getting it wrong, when you don't take the measly 5-10 minutes to understand it.
Picture the horizontal equilateral triangle formed by the centres of the three 'base' spheres.
The centre of the fourth sphere will lie directly above the centre of this triangle forming a tetrahedron with the other three centres.
The lengths of the sides of the base will be 2, and the sloping sides 3.
Now calculate the height of the tetrahedron and add 3.
Answering guest has given you an extremely good outline. Which is very similar to what i did.
Use it to your advantage.
Please no one answer more without good interaction from asker guest first.
I am not saying my final answer was necessarily correct. I did it in a hurry.