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  c1=23 c=23 30=20 cm  D=18 cm r=D/2=18/2=9 cm  V=43 π r3=43 3.1416 933053.6281 cm3 V=abd  d=V/(a b)=3053.6281/(40 35)2.1812 cm  d<cc1  x=dmm=d 10 mm=21.8116289949 mm=21.812  mm 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...):

Showing 2 comments:
#
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.

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