The internal and external diameters of a hollow hemispherical bowl are 6 cm and 10 cm, respectively. If it is melted and recast into a solid cylinder of diameter 14 cm, what is the height of the cylinder in cm?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 1.33
Internal diameter of the hemispherical shell = 6 cm
Therefore, the internal radius of the hemispherical shell = 3 cm
External diameter of the hemispherical shell = 10 cm
External radius of the hemispherical shell = 5 cm
Volume of hemispherical shell cm = 2/3π(53 - 33) = 2/3π(125 − 27) = 2/3π × 98 = 196/3π cm3
Volume of cylinder = πr2h = π × 72 × h = 49πh
Equate both volumes = 196/3π = 49πh
⇒ 196/3 = 49h
⇒ h = 196/(3 × 49) = 196/147 = 4/3 cm = 1.33