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प्रश्न
A tin maker converts a cubical metallic box into 10 cylindrical tins. The side of the cube is 50 cm and the 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 `(pi = 22/7)`
उत्तर
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 the volume of cube therefore 88% of the volume is utilized
`88/100 xx 125000 = 1250 xx 88 = 110000`cm3
Hence 110000 cm3 of cube volume is utilized to make 10 tins
Volume remains unchanged
∴ the 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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