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 $\pi=\frac{22}{7}$) ?
Answer & explanation
Correct answer: option 2
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