Three-quarters 37241

We have two cube-shaped tanks. The first has an edge of 12 dm long, and the second has an edge of 20% longer. By what % more or less water is there in the second tank if the first is three-quarters full and the second three-eighths full?

Correct answer:

p =  -13.6 %

Step-by-step explanation:

$$\begin{gathered} a=12\text{dm} \\ q=100\%+20\%=1+\frac{20}{100}=1.2 \\ b=q\cdot a=\frac{6}{5}\cdot 12=\frac{6\cdot 12}{5}=\frac{72}{5}=14.4\text{dm} \\ {V}_1=a^3=12^3=1728{\text{dm}}^3 \\ {V}_2=b^3={\frac{72}{5}}^3=2985.984{\text{dm}}^3 \\ {V}_{11}=\frac{3}{4}\cdot V_1=\frac{3}{4}\cdot 1728=\frac{3\cdot 1728}{4}=\frac{5184}{4}=1296{\text{dm}}^3 \\ {V}_{22}=\frac{3}{8}\cdot V_2=\frac{3}{8}\cdot \frac{373248}{125}=\frac{3\cdot 373248}{8\cdot 125}=\frac{1119744}{1000}=1119.744{\text{dm}}^3 \\ p=100\cdot \frac{V_{22}-V_{11}}{V_{11}}=100\cdot \frac{\frac{139968}{125}-1296}{1296}=-\frac{68}{5}\%=-13.6\% \end{gathered}$$

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