A sphere of radius 30 cm is melted and recast into hemispherical bowls, each of external radius 10 cm and wall thickness 1 cm. How many such bowls can be made? (in approx)
Show answer & explanation
Correct answer: D
Explanation
Given:
Sphere radius = 30 cm
Outer radius of the bowl = 10 cm
Thickness of the bowl = 1 cm
Inner radius of the bowl = 10 − 1 = 9 cm
By formula:
Volume of the sphere = (4/3)πR³
Volume of the semi-spherical hollow bowl = (2/3)π(R³ − r³)
Volume of the sphere = (4/3)π(30)³ = 36000π
Volume of one bowl = (2/3)π(10³ − 9³) = (542/3)π
Number of bowls = 36000π ÷ ((542/3)π)
= 36000 × 3 / 542
= 108000 / 542 = 199
Approximately 199 bowls.