A metallic solid sperical ball of radius 3 cm is melted and recast into three spherical balls. The radii of these balls are 2 cm and 1.5 cm. What is the surface area ( in cm2) of the third ball?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 25 π.
Let the radius of the third ball be r.
In this case, the volume remains constant.
The volume of big sphere = Sum of the volume of three spheres.
4/3 × π × 3 × 3 × 3 = 4/3 × π (23 + 1.53 + r3)
27 = 8 + 3.375 + r3
r = 2.5 cm.
The surface area of the sphere of radius 2.5cm = 4 × π × 2.5 × 2.5 = 25π.