Question

A cylindrical tube opened at both the ends is made of iron sheet which is 2 cm thick. If the outer diameter is 16 cm and its length is 100 cm, find how many cubic centimeters of iron has been used in making the tube?

Answer 1

According to the question,

Outer diameter d = 16 cm

Then, outer radius r = `16/2` = 8 cm

Height = Length = 100 cm

Thickness of iron sheet = 2 cm

Volume of cylinder = πr²h, where r = outer radius and π = 3.14

Thus, Volume of cylinder = πr²h

= 3.14 × (8)² × 100

= 20,096 cm³

Now, inner diameter = outer diameter – 2 × thickness of iron sheet

Inner diameter = 16 – (2 × 2) = 12 cm

Inner radius R = `12/2` = 6 cm

Thus, Volume of hollow space = πR² h, where R = inner radius and π = 3.14

= πR²h

= 3.14 × (6)² × 100

= 11,304 cm³

Thus, Volume of iron used = Volume of cylinder – Volume of hollow space

= (20,096 – 11,304) cm³

= 8800 cm³