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Ncert exemplar solutions

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?

According to the question,

Outer diameter d = 16cm

Then,

Outer radius r – 16/2 = 8cm

Height = length = 100cm

Thickness of iron sheet = 2cm

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) = 12cm

Inner radius R = 12/2 = 6cm

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

= πR2 h

= 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

According to the question,

Outer diameter d = 16cm

Then,

Outer radius r – 16/2 = 8cm

Height = length = 100cm

Thickness of iron sheet = 2cm

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) = 12cm

Inner radius R = 12/2 = 6cm

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

= πR2 h

= 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

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