MAH-CET 2020 Geometry & Mensuration — Previous Year Question

In the given question, two quantities are given, one as 'Quantity I' and another as 'Quantity II'. Determine the relationship between the two quantities and choose the appropriate option:

Quantity I: A man has two solid balls. The ratio between the radius of the first ball and the second ball is 4 : 3. If the man cuts the second ball from the middle, then the difference between the total surface area of the first ball and the total surface area of a part (hemisphere) of the second ball is 1424.5 $cm^2$. Find the radius of the bigger ball. Quantity II: The height of a cylindrical vessel is equal to the side of a square having area 256 $cm^2$. If the volume of the cylindrical vessel is 22176 $cm^3$, find the radius of the cylindrical vessel.