Final answer:
To recast the hollow cylinder, first calculate the volume of the hollow cylinder and then use that information to find the volume of the solid cylinder.
The length of the solid cylinder required is approximately 3567.54 cm.
Step-by-step explanation:
The volume of the hollow cylinder can be calculated using the formula V = πR²h - π(r+ t)²h, where R is the external radius, r is the internal radius, h is the length or height, and t is the thickness.
Using the given values, we have R = 20 cm/2 = 10 cm, r = (20 cm - 4 mm)/2 = 9.8 cm and h = 32 cm.
Calculating these values gives us a volume of approximately 44,823.9 cm³.
Now, to find the volume of the solid cylinder, we can use the formula V = πr²h, (where r is the radius and h is the height or length).
Since the diameter of the solid cylinder is given as 4 cm, its radius would be 4 cm/2 = 2 cm.
Assuming the length of the solid cylinder is L, we can set up the equation 44,823.9 cm³ = π(2 cm)²L and solve for L.
44,823.9 cm³ = π(2 cm)²L
44,823.9 cm³ = 4πL cm²
L = 44,823.9 cm³ / (4π cm²)
L ≈ 3567.54 cm
Therefore, a solid right circular cylinder with a length of approximately 3567.54 cm is required to recast this hollow cylinder.