NCERT Exemplar Solutions Class 9 Mathematics Solutions for Surface Areas and Volumes - Exercise 13.4 in Chapter 13 - Surface Areas and Volumes
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
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