# 003 Weight of an iron shell

**Example 003**

An iron ball 10 cm in diameter weighs 4 kg. Find the weight of an iron shell 5 cm thick whose external diameter is 50 cm.

**Solution 003**

Unit weight of iron

$\gamma = \dfrac{W}{V}$

$\gamma = \dfrac{W}{V}$

$\gamma_{iron} = \dfrac{4}{\frac{4}{3}\pi (5^3)}$

$\gamma_{iron} = \dfrac{3}{125\pi} \, \text{ kg/cm}^3$

Radii of iron shell (R = external radius and r = internal radius)

$R = \frac{1}{2}(50)$

$R = 25 \, \text{ cm}$

$r = R - t = 25 - 5$

$r = 20 \, \text{ cm}$

Volume of iron shell

$V = \frac{4}{3}\pi (R^3 - r^3)$

$V = \frac{4}{3}\pi (25^3 - 20^3)$

$V = \dfrac{30\,500\pi}{3} \, \text{ cm}^3$

Weight of iron shell

$W = \gamma_{iron} V = \dfrac{3}{125\pi} \left( \dfrac{30\,500\pi}{3} \right)$

$W = 244 \, \text{ kg}$ *answer*

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