three spheres of diameter 2,3 & 4cms formed into a single sphere.Find the diameter of the new sphere assuming that the volume of a sphere is proportional to the cube of diameter.

Answer 1

volume of the original spheres
= (4/3)π (1^3 + (3/2)^3 + 2^3)
= (4/3)(99/8)π or 16.5π

radius of big sphere ---> r cm

(4/3)π r^3 = (4/3)(99/8) π
r^3 = 99/8
r = 99^(1/3)/2 or the cuberoot of 99 /2

diameter = 2r = cuberoot(99) = appr 4.626 cm