Aquarium

The box-shaped aquarium is 40 cm high; the bottom has dimensions of 70 cm and 50 cm. Simon wanted to create an exciting environment for the fish, so he fixed three pillars to the bottom. They all have the shape of a cuboid with a square base. The base edge of each block is 10cm long. The heights of the blocks are 10cm, 20cm, 30cm. How many liters of water should be poured into the aquarium to reach a height of 25cm?

Result

V =  81.5 l

Solution:

$a = 70 \ cm = 70 / 10 \ dm = 7 \ dm \ \\ b = 50 \ cm = 50 / 10 \ dm = 5 \ dm \ \\ c = 25 \ cm = 25 / 10 \ dm = 2.5 \ dm \ \\ \ \\ V_{ 1 } = a \cdot \ b \cdot \ c = 7 \cdot \ 5 \cdot \ 2.5 = \dfrac{ 175 }{ 2 } = 87.5 \ dm^3 \ \\ \ \\ x = 10 \ cm = 10 / 10 \ dm = 1 \ dm \ \\ o = (10+20+30)/10 = 6 \ dm \ \\ \ \\ V_{ 2 } = x \cdot \ x \cdot \ o = 1 \cdot \ 1 \cdot \ 6 = 6 \ dm^3 \ \\ \ \\ V = V_{ 1 }-V_{ 2 } = 87.5-6 = \dfrac{ 163 }{ 2 } = 81.5 = 81.5 \ \text { l }$

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