in this case if we consider the relationship between the centres of the spheres, the problem reduces to one involving a pyramid.

first consider three spheres, each of radius 10 cm, touching each other as shown:

if the centers of the spheres are P, Q, R and S be the mid-point of QR.

in the right angled triangle PSR,

in the 2nd diagram P, Q, R, T and U represent the centres of the spheres.

while S represent the mid-point of QR. and 

let V be the centre of the squareQRTU.


using pythagoras' theorem in triangle PVS,

the height of the centre V of the square QRTU from the ground = 10 cm

therefore the height of the centre of the fifth sphere =