Stones in aquarium

The water is up to three-quarters of the depth in an aquarium with a length of 2 m, 1.5 m wide, and 2.5 m deep. 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:

$$\begin{gathered} a=2\text{m} \\ b=1.5\text{m} \\ c=2.5\text{m} \\ V=a\cdot b\cdot c=2\cdot 1.5\cdot 2.5=\frac{15}{2}=7\frac{1}{2}=7.5{\text{m}}^3 \\ {V}_1=\frac{3}{4}\cdot V=\frac{3}{4}\cdot \frac{15}{2}=\frac{3\cdot 15}{4\cdot 2}=\frac{45}{8}=5.625{\text{m}}^3 \\ {V}_2=V_1+2=\frac{45}{8}+2=\frac{45}{8}+\frac{2\cdot 8}{8}=\frac{45}{8}+\frac{16}{8}=\frac{45+16}{8}=\frac{61}{8}=7.625{\text{m}}^3 \\ {V}_2>V \\ x=0 \end{gathered}$$

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