Given,
Radius of first solid sphere (r1) = 2 cm
Radius of second solid sphere (r2) = 4 cm
Height of cone (h) = 8 cm
Let radius of cone be r cm.
Since, two spheres are melted and recasted into cone.
∴ Volume of 1st sphere + Volume of 2nd sphere = Volume of cone
⇒34π(r1)3+34π(r2)3=31πr2h⇒4(r1)3+4(r2)3=r2h⇒r2=h4r13+4r23⇒r2=84×23+4×43⇒r2=84×8+4×64⇒r2=832+256⇒r2=8288⇒r2=36⇒r=36⇒r=6 cm.
Hence, the radius of cone formed = 6 cm.