Block edge change

The block has 10 cm, 20 cm, and 50 cm dimensions. We reduce the first edge of the cuboid by 20% and increase the second by 20%. How does the volume of the cuboid change? By how many percent?

Final Answer:

p =  -4 %

Step-by-step explanation:

$$\begin{gathered} a=10\text{cm} \\ b=20\text{cm} \\ c=50\text{cm} \\ {V}_1=a\cdot b\cdot c=10\cdot 20\cdot 50=10000{\text{cm}}^3 \\ {r}_1=100\%-20\%=1-\frac{20}{100}=0.8 \\ {r}_2=100\%+20\%=1+\frac{20}{100}=1.2 \\ A=r_1\cdot a=0.8\cdot 10=8\text{cm} \\ B=r_2\cdot b=1.2\cdot 20=24\text{cm} \\ C=c=50\text{cm} \\ {V}_2=A\cdot B\cdot C=8\cdot 24\cdot 50=9600{\text{cm}}^3 \\ p=\frac{V_2-V_1}{V_1}\cdot 100=\frac{9600-10000}{10000}\cdot 100=-4\% \end{gathered}$$

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