# 015 Two unequal balls inside the cylinder

**Example 015**

Two balls, one 15 cm in diameter and the other 10 cm in diameter, are placed in a cylindrical jar 20 cm in diameter, as shown in Figure 014. Find the volume of water necessary to cover them.

**Solution 015**

$x = 20 - 5 - 7.5$

$x = 7.5 \, \text{ cm}$

$h^2 + x^2 = (5 + 7.5)^2$

$h^2 + 7.5^2 = 12.5^2$

$h = 10 \, \text{ cm}$

Depth of water

$H = 7.5 + h + 5$

$H = 7.5 + 10 + 5$

$H = 22.5 \, \text{ cm}$

Volume of water

$V_{water} = V_H - V_{balls}$

$V_{water} = \frac{1}{4}\pi (20^2)(22.5) - \frac{4}{3}\pi (7.5^3 + 5^3)$

$V_{water} = 4777.84 \, \text{ cm}^3$ *answer*

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