Pebble

The aquarium is filled with two-thirds water with internal dimensions of the bottom 40 cm × 35 cm and a height of 30 cm. Calculate how many millimeters the water level in the aquarium rises by dipping a pebble-shaped sphere with a diameter of 18 cm.

Correct answer:

x =  21.8116 mm

Step-by-step explanation:

$$\begin{gathered} a=40\text{cm} \\ b=35\text{cm} \\ c=30\text{cm} \\ {c}_1=\frac{2}{3}\cdot c=\frac{2}{3}\cdot 30=\frac{2\cdot 30}{3}=\frac{60}{3}=20\text{cm} \\ D=18\text{cm} \\ r=D/2=18/2=9\text{cm} \\ V=\frac{4}{3}\cdot \pi \cdot r^3=\frac{4}{3}\cdot 3.1416\cdot 9^3\doteq 3053.6281{\text{cm}}^3 \\ V=abd \\ d=V/(a\cdot b)=3053.6281/(40\cdot 35)\doteq 2.1812\text{cm} \\ d<c-c_1 \\ x=d\to \text{mm}=d\cdot 10\text{mm}=2.1812\cdot 10\text{mm}=21.812\text{mm}=21.8116\text{mm} \end{gathered}$$

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