Three metallic spheres with radii 3 cm, 4 cm, and 5 cm respectively are melted together and recast into a single solid sphere. What is the radius of the new sphere?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 6 cm.
Volume of a sphere = (4/3)πr3
Volume of the three spheres = (4/3)π(33 + 43 + 53)
= (4/3)π(27 + 64 + 125)
= (4/3)π × 216
= 288π cm3
Let the radius of the new sphere = R cm
(4/3)πR3 = 288π
⇒ R3 = 216
⇒ R = 6 cm