Aquarium 7098

The zoo has an aquarium with a length of 2.5 m, a width of 1.5 m, and a depth of 2 m. The water reaches 3/4 of the height of the aquarium. Can we put a 2 m³ stone in the aquarium without the water spilling out of the aquarium? (1=Yes, 0=No)

Correct answer:

x =  0

Step-by-step explanation:

$$\begin{gathered} a=2.5\text{m} \\ b=1.5\text{m} \\ c=2\text{m} \\ {V}_1=a\cdot b\cdot c=2.5\cdot 1.5\cdot 2=\frac{15}{2}=7\frac{1}{2}=7.5{\text{m}}^3 \\ {V}_2=\frac{3}{4}\cdot V_1=\frac{3}{4}\cdot \frac{15}{2}=\frac{3\cdot 15}{4\cdot 2}=\frac{45}{8}=5.625{\text{m}}^3 \\ {V}_3=V_2+2=\frac{45}{8}+2=\frac{45}{8}+\frac{2\cdot 8}{8}=\frac{45}{8}+\frac{16}{8}=\frac{45+16}{8}=\frac{61}{8}=7.625{\text{m}}^3 \\ {V}_3>V_1 \\ x=0 \end{gathered}$$

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