3 solid spheres of diameters 6 cm, 8 cm and 10 cm are melted together to form a single solid sphere. Find its radius.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 6 cm.
The volume of a sphere = (4/3)πr3 where r is the radius of the sphere
Diameter of the first sphere = 6 cm
So, the radius of the first sphere = 6/2 = 3 cm
Diameter of the second sphere = 8 cm
So, the radius of the second sphere = 8/2 = 4 cm
Diameter of the third sphere = 10 cm
So, the radius of the third sphere = 10/2 = 3 cm
Let R be the radius of the new sphere.
So, (4/3)πR3 = (4/3)π(3)3 + (4/3)π(4)3 + (4/3)π(5)3 = 288π
⇒ R3 = 216
⇒ R = ∛216 = 6
Therefore, the radius of the new sphere is 6 cm.