Given,
Internal diameter of the hollow sphere = 6 cm
So, the internal radius of the hollow sphere = 6/2 cm = 3 cm = r
External diameter of the hollow sphere = 10 cm
So, the external radius of the hollow sphere = 10/2 cm = 5 cm = R
We know that,
Volume of the hollow spherical shell = 4/3 π × (R3 – r3)
= 4/3 π × (53 – 33) ….. (i)
And given, the length of the solid cylinder = 8/3 cm
Let the radius of the solid cylinder be r cm
We know that,
Volume of the cylinder = π × r2 × h
= π × r2 × 8/3 ….. (ii)
Now equating both (i) and (ii), we have
4/3 π × 53 – 33 = π × r2 × 8/3
4/3 x (125 – 27) = r2 × 8/3
98/2 = r2
r2 = 49
r = 7
So, d = 7 x 2 = 14 cm
Therefore, the diameter of the cylinder is 14 cm.