Question

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)`

Answer 1

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