Question

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

Answer 1

Cross-sectional area of iron tube = 192 cm³ / 8 cm = 24 cm²
A = s² - 5² = 24 cm²
s² = 25 + 24 = 49 cm²
s = √(49 cm²) = 7 cm
thickness = ½(7 - 5) = 1 cm

Answer 2

Answer :

• The thickness of the tube is 1 cm.

Step-by-step explanation :

Given :

• The internal square is of 5cm side.

• The length of the tube is 8 cm.

• There are 192 cm³ of iron in this tube.

To find :

• Its thickness = ?

Since the internal square is of 5 cm side and the length of the tube is 8cm .

∴ Its internal volume = 5x5x8 cm³= 200 cm³ .

Let the thickness of a side be x cm . Then the external square is of ( 5 + 2x ) cm side .

As the tube is open at both ends , its length remains 8 cm .

∴ The external volume of the tube = ( 5 + 2x ) ( 5 + 2x ) x 8 cm³.

Since the volume of iron in the tube is 192 cm³ ,

∴ ( 5 + 2x )² x 8 - 200 = 192

➽ ( 5 + 2x ) 2x8 = 392

➽ ( 5 + 2x )² = 49

➽ 5 + 2x = 7

➽ 2x = 7 - 5

➽ 2x = 2

➽ x = 1 .

∴ The thickness of the tube = 1 cm .