MathematicsFind the weight of a lead pipe 3.5 m long, if the external diameter of the pipe is 2.4 cm and the thickness of the lead is 2 mm and 1 cu cm of lead weighs 11 g .

Find the weight of a lead pipe 3.5 m long, if the external diameter of the pipe is 2.4 cm and the thickness of the lead is 2 mm and 1 cu cm of lead weighs 11 g .


  1. A
    5324g
  2. B
    4235g
  3. C
    5234g
  4. D
    5423g 

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    Solution:

    Given:
    seoLet us assume the height of the lead pipe is h , the external diameter of the lead pipe is D , thickness of the lead pipe is t and the weight of 1 cubic centimeters of lead is w .
    The height of the lead pipe
     ⇒h=3.5 m
    ⇒h=350 cm
    The external diameter of the pipe
     ⇒D=2.4 cm
    So, the external radius (R) of the pipe
    R=D2
    R=2.42
    R=1.2 cm
    Thickness of the lead pipe
     t=2 mm
    ⇒t=0.2 cm
    So, the inner radius (r) of the pipe
     ⇒r=(R−t)
    ⇒r=(1.2−0.2)
    ⇒r=1 cm
    Also given,
    The weight of 1 cu cm lead w=11 g
    We know that the lead pipe is equivalent to a hollow cylinder. So, the volume of the lead pipe is equal to the volume of the hollow cylinder.
    The formula for the hollow cylinder is given by –
     V=π(R2−r2)h
    Substituting the values in this formula we get,
     V=227×1.22-12×350
    V=484 cm3
    Now we know that the weight of 1 cm3 lead w=11 g .
    So, the weight of 484 cm3 lead will be
     ⇒W=484×w
    ⇒W=484×11 g
    ⇒W=5324 g
    Therefore, the total weight of the given lead pipe is 5324 g .
    So, the correct answer is “ 5324 g ”.
     
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