Decreases 5625

How much percent will the surface and volume of the cube decrease if the diagonal decreases by 10%?
b) if the diagonal increases by 10%?

Correct answer:

p₁ =  19 %
p₂ =  27.1 %
p₃ =  21 %
p₄ =  33.1 %

Step-by-step explanation:

$$\begin{gathered} S=K_1.u^2 \\ p=1-10/100=\frac{9}{10}=0.9 \\ q=p^2=0.9^2=\frac{81}{100}=0.81 \\ {p}_1=(1-q)\cdot 100=(1-0.81)\cdot 100=19\% \end{gathered}$$

$$\begin{gathered} V=K_2.u^3 \\ {p}_2=(1-p^3)\cdot 100=(1-0.9^3)\cdot 100=27.1\% \end{gathered}$$

$$\begin{gathered} k=1+10/100=\frac{11}{10}=1.1 \\ {p}_3=(k^2-1)\cdot 100=(1.1^2-1)\cdot 100=21\% \end{gathered}$$

$p_4=(k^3-1)\cdot 100=(1.1^3-1)\cdot 100=33.1\%$

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