Question : Three spherical balls of radius 2 cm, 4 cm, and 6 cm are melted to form a new spherical ball. In this process, there is a loss of 25% of the material. What is the radius (in cm) of the new ball?
Option 1: 6
Option 2: 8
Option 3: 12
Option 4: 16
Correct Answer: 6
Solution :
Given: The radii of three spherical balls are 2 cm, 4cm, and 6cm.
Percentage loss of material during melting = 25%
Let the radius of the new ball be
So, Percentage of usable material = 75%
Volume of sphere =
Total volume of three spheres = Volume lost + volume of new ball
Volume of new ball =
⇒
⇒ R =
⇒ R = 6 cm
Hence, the correct answer is 6.