Question

The external diameter of a lead pipe is 2.4 cm and the thickness of the lead is 2mm .Find the weight of the pipe of length 7 m it being given that 1 cm3 of lead weighs 10g

Answer 1

Answer :

• 9.68 kg

Step-by-step explanation:

Given :

• Diameter of lead pipe is = 2.4 cm

• Thickness of lead is = 2 mm.

To find :

• The weight of the pipe of length 7 m it being given that 1cm³ of lead weighs 10g.

$\tt Let\: r_1\: and\: r_2\: be \\ \tt the\: internal\: and \:external\: radii\: of \\ \tt the \:pipe. \\ \\\therefore \tt r^2 = \dfrac{2.4}{2}cm = 1.2 cm\\ \\ \tt and \:r_1 = \left(1.2 - \dfrac{2}{10}\right)\: cm = 1 cm\\ \\ \tt and \:h = (7\times 100) = 700 \:cm. \\ \\ \therefore \tt Volume\: of\: pipe = \pi(r^2_2 - r^2_1)h \:and \\ \\ \tt weight \:of\: lead \:of\: 1cm^3 = 10g\\ \\ \tt weight \:of \:pipe = 10 \times \pi(r^2_2 - r^2_1)h\\ \\ \tt \implies \left[10\times \dfrac{22}{7}{(1.2)^2 - (1)^2}\times 700 \right]\: g \\ \\ \tt \implies (22000\times 0.44) \times \dfrac{1}{1000}\:kg\\ \\ \tt \implies {\green {9.68 \:kg}} .$