Question
Radius of a cylindrical vessel is 3cm less than breadth
of rectangle, while height of cylindrical vessel is equal to length of rectangle, whose area is 720 cm². If ratio between length & breadth of rectangle is 5:4, then find the thickness of 1 disc, if these discs are kept one above another in cylindrical vessel and 15 discs get completely fit in cylindrical vessel.(Let radius of discs equal to radius of cylindrical vessel)?Solution
Let length & breadth of rectangle be 5x & 4x respectively Given area of rectangle = 720 cm2 5x × 4x = 720 cm2 20x2 = 720 x2 = 36 x = 6 cm Radius of cylindrical vessel = 4 × 6 − 3 = 21 cm Height of cylindrical vessel = 5 × 6 = 30 cm Volume of cylindrical vessel = π × 21 × 21 × 30 = 13230 π cm3 Let thickness of each discs be x cm So, 15 × π × x × 21 × 21 = 13230 π cm3 x = 13230/(441 x 15) x = 2 cm
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