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प्रश्न
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?
उत्तर
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
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