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

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5.234kg

5.324kg

5.432kg

5.342kg

answer is B.

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Detailed Solution

Given:

Let us assume the height of the Cylindrical pipe is h , the external diameter of the Cylindrical pipe is D , thickness of the Cylindrical pipe is t and the weight of 1 cubic centimeters of Cylindrical is w .
The height of the Cylindrical 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=D/2
⇒R=2.4/2
⇒R=1.2 cm
Thickness of the Cylindrical 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 Cylindrical w=11 g
We know that the Cylindrical 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,

\Rightarrow V = \frac{22}{7} \times ({1.2}^{2} - 1^{2}) \times 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 = 5.324kg”.

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