Two balls

Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.

Correct answer:

V =  5322.6258 cm³

Step-by-step explanation:

$$\begin{gathered} r=8 \\ R=6 \\ x=2\cdot 10-r-R=2\cdot 10-8-6=6 \\ h=\sqrt{(r+R{)}^2-x^2}=\sqrt{(8+6{)}^2-6^2}=4\sqrt{10}\doteq 12.6491 \\ H=h+r+R=12.6491+8+6\doteq 26.6491 \\ {V}_1=\pi \cdot 10^2\cdot H=3.1416\cdot 10^2\cdot 26.6491\doteq 8372.065 \\ {V}_2=4/3\pi \cdot r^3=4/3\cdot 3.1416\cdot 8^3\doteq 2144.6606 \\ {V}_3=4/3\pi \cdot R^3=4/3\cdot 3.1416\cdot 6^3\doteq 904.7787 \\ V=V_1-V_2-V_3=8372.065-2144.6606-904.7787=5322.6258{\text{cm}}^3 \end{gathered}$$

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