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Question 1 Surface Areas and Volumes - Exercise 13.4

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:

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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