Question
Height of a cylindrical vessel is equal to side of a
square, whose area is 324cm². Radius of cylindrical vessel is equal to average of radius of a sphere and hemisphere. If ratio between the radius of hemisphere and that of the sphere is 2:1 and difference between their total surface area is 1232 cm², then find volume of cylindrical vessel?Solution
Given, height of cylindrical vessel = side of square   a² = 324cm²  a = 18 cm   Let radius of hemisphere is 2r cm and sphere is r cm.    According to question, 3π(2r)² – 4πr² = 1232 cm² 12r² – 4r² = 392   r² = 49 or r = 7   Radius of cylindrical vessel = (14 + 7)/2 = 10.5 cm   Volume of cylindrical vessel = (22/7) × 10.5 × 10.5 × 18 = 6237cm³
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