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:

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

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