The weight of a lead pipe 3.5m long, if the external diameter of the pipe is 2.4cm the thickness of the lead is 2mm and 1 cubic cm of lead weight 11gm is
Question
The weight of a lead pipe 3.5m long, if the external diameter of the pipe is 2.4cm the thickness of the lead is 2mm and 1 cubic cm of lead weight 11gm is
Solution
To solve this problem, we need to find the volume of the lead in the pipe and then multiply it by the weight of 1 cubic cm of lead. Here are the steps:
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First, convert all measurements to the same unit. In this case, we'll use cm. So, the length of the pipe is 350 cm (since 1m = 100cm), the external diameter is 2.4 cm, and the thickness of the lead is 0.2 cm (since 1cm = 10mm).
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The internal diameter of the pipe is the external diameter minus twice the thickness of the lead. So, it's 2.4 cm - 2*0.2 cm = 2 cm.
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The volume of a cylinder (which is the shape of the pipe) is πr²h, where r is the radius and h is the height. The volume of the lead in the pipe is the volume of the pipe with the external diameter minus the volume of the pipe with the internal diameter.
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The external radius is half the external diameter, so it's 2.4 cm / 2 = 1.2 cm. The internal radius is half the internal diameter, so it's 2 cm / 2 = 1 cm. The height is the length of the pipe, so it's 350 cm.
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The volume of the pipe with the external diameter is π*(1.2 cm)²*350 cm = 1584 cm³ (approximately).
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The volume of the pipe with the internal diameter is π*(1 cm)²*350 cm = 1100 cm³ (approximately).
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The volume of the lead in the pipe is the difference between these two volumes, so it's 1584 cm³ - 1100 cm³ = 484 cm³.
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Finally, the weight of the lead in the pipe is the volume of the lead times the weight of 1 cubic cm of lead. So, it's 484 cm³ * 11 gm/cm³ = 5324 gm, or 5.324 kg.
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