Q5 of 23 Page 1

Solve any two sub-questions:

A tin maker converts a cubical metallic box into 10 cylindrical tins. Side of the cube is 50 cm and radius of the cylinder is 7 cm. Find the height of each cylinder so made, if the wastage of 12% is incurred in the process




Side of cube = a = 50 cm


Volume of cube = V = a3 = 503 = 125000 cm3


Radius of cylinder = r = 7 cm


Height of cylinder = h cm


Volume of cylinder = πr2h


= (22/7) × 72 × h


= 154h cm3


10 cylinder tins are made


Total volume of cylinders = 10 × 154h


= 1540h cm3


Wastage of 12% of volume of cube therefore 88% of volume is utilized



Hence 110000 cm3 of cube volume is utilized to make 10 tins


Volume remains unchanged


∴ volume of cube utilized = Total volume of cylinders


∴ 110000 = 1540h


∴ 11000 = 154h


∴ h = 11000/154


∴ h = 71.428 cm


Height of cylinder = 71.428 cm


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