False
Explanation:
Let the radius of sphere = r
When a solid ball is exactly fitted inside the cubical box of side a,
We get,
Diameter of ball = Edge length of cube
2r = a
Radius, r = a/2
We also know that,
Volume of sphere = 4/3πr3
Volume of ball = 4/3π(a/2)3 = 4/3π(a3/8) = 1/6πa3