Question

A hollow square-shaped tube open at both ends is made of iron. The internal square is of 5 cm side and the length of the tube is 8 cm. There are 192 cm³ of iron in this tube. Find its thickness.

Answer 1

Given that the volume of the iron in the tube 192 cm³
Let the thickness of the tube = x cm
Side of the external square = ( 5 + 2x ) cm

∵ Ext. vol. of the tube its internal vol.= volume of iron in the tube, we have,
( 5 + 2x )( 5 + 2x ) x 8 - 5 x 5 x 8 = 192
( 25 + 4x² + 20x ) x 8 - 200 = 192
200 + 32x² + 160x - 200 = 192
32x² + 160x - 192 = 0
x² + 5x - 6 = 0
x² + 6x - x - 6 = 0
x( x + 6 ) - ( x + 6 ) = 0
( x + 6 )( x - 1 ) = 0
( x - 1 ) = 0
x = 1
Therefore, thickness is 1 cm.