If 125 identical small spheres are made from a solid sphere of diameter 15 cm, then what is the surface area of each of the small spheres?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 9π cm2.
Volume of Sphere = 4/3πr13
where r1 = radius of the big sphere
Diameter = 15 so, radius = 15/2 = 7.5 cm
Volume of large sphere = 4/3 × π × 15/2 × 15/2 × 15/2 = 13500π/24 = 1125π/2
The volume of a spherical ball = Volume of a large sphere/125
The volume of a spherical ball = 1125π/2 × 1/125
4/3πr23 = 9/2π
r23 = 27/8
r2 = 3/2 = 1.5
The surface area of the small sphere = 4πr22
4 × π × 3/2 × 3/2 = 9π cm2