# 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.

Result

x =  21.812 mm

#### Solution:

$a = 40 \ cm \ \\ b = 35 \ cm \ \\ c = 30 \ cm \ \\ \ \\ c_{ 1 } = \dfrac{ 2 }{ 3 } \cdot \ c = \dfrac{ 2 }{ 3 } \cdot \ 30 = 20 \ cm \ \\ \ \\ D = 18 \ cm \ \\ r = D/2 = 18/2 = 9 \ cm \ \\ \ \\ V = \dfrac{ 4 }{ 3 } \cdot \ \pi \cdot \ r^3 = \dfrac{ 4 }{ 3 } \cdot \ 3.1416 \cdot \ 9^3 \doteq 3053.6281 \ cm^3 \ \\ V = abd \ \\ \ \\ d = V/(a \cdot \ b) = 3053.6281/(40 \cdot \ 35) \doteq 2.1812 \ cm \ \\ \ \\ d < c-c_{ 1 } \ \\ \ \\ x = d \rightarrow mm = d \cdot \ 10 \ mm = 21.8116289949 \ mm = 21.812 \ \text { mm }$

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Math student
where did we get the small d?

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

#### Following knowledge from mathematics are needed to solve this word math problem:

Do you know the volume and unit volume, and want to convert volume units?

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