A solid hemisphere has radius 14 cm. It is melted to form a cylinder such that the ratio of its curved surface area and total surface area is 2 : 3. What is the radius (in cm) of its base?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 14/∛3
Radius of hemisphere = R = 14 cm
let r and h be the radius and height of the cylinder
AQ
2πrh/2π(r + h) = 2/3
h/r + h = 2/3
3h = 2h + 2r
h = 2r
Volume of sphere = Volume of cylinder
2/3 × π × R3 = πr2 × 2r
143/3 = r3
r = 14/ ∛3 cm