Pebble

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

Correct result:

x =  21.8116 mm

Solution:

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

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Showing 2 comments:

Math student

where did we get the small d?

1 year ago  Like

Dr Math

small d = height of water level rise. c is occupied yet, thus the next variable is d.

1 year ago  Like

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