The smallest enclosing cylinder for a sphere of radius r has base radius r and height 2r, with volume 2πr³. The sphere volume is (4/3)πr³, exactly two-thirds of the cylinder’s volume.
Class 9 Ganita Manjari Part 2 book Chapter 14 Question Answer
Chapter 14 Math of Space Surface Area and Volume (Ganita Manjari 2) Solutions
Consider a sphere of radius r, which has volume (4/3)πr³. The smallest cylinder enclosing this sphere must have a base radius equal to r and a height equal to the sphere’s diameter, 2r. The cylinder’s volume is πr²(2r) = 2πr³. Comparing volumes gives [(4/3)πr³] / [2πr³] = 2/3.
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