Stones in aquarium

In an aquarium with a length of 2 m, 1.5 m wide, and 2.5 m deep, the water is up to three-quarters of the depth. Can we place 2m cubic meters of stones in the aquarium without spilling water? (0 = no, 1 = yes)

Correct answer:

x =  0

Step-by-step explanation:

$$\begin{gathered} a=2\text{ m } \\ b=1.5\text{ m } \\ c=2.5\text{ m } \\ V=a\cdot b\cdot c=2\cdot 1.5\cdot 2.5={\displaystyle \frac{15}{2}}=7\frac{1}{2}=7.5{\text{m}}^3 \\ {V}_1={\displaystyle \frac{3}{4}}\cdot V={\displaystyle \frac{3}{4}}\cdot 7.5={\displaystyle \frac{45}{8}}=5\frac{5}{8}=5.625{\text{m}}^3 \\ {V}_2=V_1+2=5.625+2={\displaystyle \frac{61}{8}}=7\frac{5}{8}=7.625{\text{m}}^3 \\ {V}_2>V \\ x=0 \end{gathered}$$

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