External diameter of shell = 24cm and

Internal diameter of shell = 18cm

So,

External radius of shell = 12 cm and

Internal radius = 9 cm

Volume of lead in the shell = π[12³–9³]cm³

Let the radius of the cylinder be r cm

Height of the cylinder = 37 cm

Volume of the cylinder = πr²h = πr²(37)

π[12³–9³] = πr² × 37

π × 999 = πr² × 37

r² = × π × 999 × π = 36cm²

r = = 6cm

Hence, diameter of the base of the cylinder = 12 cm