Question

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

Answer 1

SOLUTION:-

Given:

A hollow square shaped tube Open at both ends is made up of iron.

•The internal square is of 5cm side.

•The length of the tube is 8cm.

•The volume of iron tube is 192cm³.

To find:

The thickness of the iron tube.

Explanation:

Let the thickness of the tube be R cm.

Therefore,

•Side of the outer square= (R+5)cm.

Tube is in the form of hollow cuboid:

•Volume of the outer cuboid

=) 8×(R+5) ×(R+5)cm³

=) 8 ×(R+5)²

•Volume of the inner cuboid

=) 8 ×5 ×5

=) 200cm³

NOW,

Volume of the iron Tube:

Volume of outer cuboid - inner cuboid

So,

=) 8(R+5)² - 200=192

=) 8(R+5)² = 192 +200

=) 8(R+5)² = 392

=) (R+5)² = 49

=) R+5 = √49

=) R+5 = 7

=) R= 7 -5

=) R= 2cm.

Thus,

The thickness of the iron tube is 2cm.

Thank you.