A hollow square-shaped tube open at both ends is made of iron. The internal square is of 5cm side and the length of the tube is 8cm. There are 192cm^3 of iron in this tube. Find its thickness.
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Answer:
Side of the inner square = 5 cm
Length of the tube = 8 cm
Volume of metal in the tube = 192 cm2
Let the thickness of the tube be x cm.
∴ Side of the outer square = (x + 5) cm
The tube is in the form of a hollow cuboid.
Volume of the outer cuboid = 8 × (x + 5) × (x + 5) cm3 = 8 (x + 5)2cm3
Volume of the inner cuboid = 8 × 5 × 5 cm3 = 200 cm3
Volume of metal in the tube = Volume of outer cuboid – Volume of inner cuboid
8(x+5)^2 - 200 = 192
8(x+5)^2 = 392
(x+5)^2 = 49
x+5 = 7
x = 2
Thus, the thickness of the tube is 2 cm.
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