Question

Three spheres of diameters 2, 3 and 4 cms. respectively 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 its diameter.

Answer 1

Explanation:

Down vote

Let V1=αD31 be the volume of the first sphere, α being the proportional factor between volume and the cube of the diameter of the sphere.

Define V2 and V3 accordingly.

Then the last shpere whose volume is the sum of the other three has a volume V4

V4=V1+V2+V3

αD34=αD31+αD32+αD33

D4=(D31+D32+D33)1/3

You replace D1=2cm, D2=3cm, D3=4cm and you get your result in cm.