What is the radius of the circular plate of thickness 1 cm made by melting a…

Step 1: Compute the sphere's volume. Volume of sphere = (4/3)πr^3 = (4/3)π·3^3 = (4/3)π·27 = 36π cubic cm.

Step 2: Express the plate's volume. The plate is a cylinder of thickness 1 cm, so Volume of plate = π·R^2·h with h = 1 cm, hence π·R^2·1 = π·R^2.

Step 3: Equate volumes and solve for R.

• π·R^2 = 36π

• R^2 = 36 ⇒ R = 6 cm

Answer: 6 cm.