A solid hemisphere has radius 21 cm. It is melted to form a cylinder such that the ratio of its curved surface area to total surface area is 2 : 5. What is the radius (in cm) of its base(take $\pi=\frac{22}{7}$) ?

21

We know that,

The curved surface area of the cylinder = 2πRh

The total surface area of cylinder = 2πR(R + h)

The volume of the cylinder = πR²h

The volume of the solid hemisphere = 2/3πr³ 

(where r is the radius of a solid hemisphere and R is the radius of a cylinder)

According to the question,

CSA/TSA = 2/5

= [2πRh]/[2πR(R + h)] = 2/5

= h/(R + h) = 2/5

= 5h = 2R + 2h

= h = (2/3)R .......(1)

The cylinder's volume and the volume of a solid hemisphere are equal.

= πR²h = (2/3)πr³

= R2 × (2/3)R = (2/3) × (21)³

= R³ = (21)3

= R = 21 cm