# Brass tube

The outer perimeter of brass tube (ρ = 8.5 g/cm3) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness?

Result

h =  2.938 mm

#### Solution:

$o = 2\pi r \ \\ r = 38/(2\pi) = 6.048 cm \ \\ V = m/ \rho = 588.235 \ cm^3 \ \\ (\pi r^2-\pi (r-h)^2)54 = V \ \\ r^2 - (r-h)^2 = V/\pi/54 \ \\ - (r-h)^2 = V/\pi - r^2 \ \\ (r-h)^2 = r^2 - V/\pi/54 \ \\ r-h = \sqrt { 33.111 } \ \\ r-h = 5.754 \ \\ h = (6.048 - 5.754) \ cm = 2.938 \ \text{ mm }$

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