The surface area

How much percent will the surface area of a 4x5x8 cm block increase if the length of the shortest edge is increased by 2 cm?

Correct answer:

p =  28.2609 %

Step-by-step explanation:

$$\begin{gathered} a=4\text{ cm } \\ b=5\text{ cm } \\ c=8\text{ cm } \\ {a}_1=2+a=2+4=6\text{ cm } \\ {S}_1=2\cdot (a\cdot b+b\cdot c+c\cdot a)=2\cdot (4\cdot 5+5\cdot 8+8\cdot 4)=184{\text{cm}}^2 \\ {S}_2=2\cdot (a_1\cdot b+b\cdot c+c\cdot a_1)=2\cdot (6\cdot 5+5\cdot 8+8\cdot 6)=236{\text{cm}}^2 \\ p=100\cdot {\displaystyle \frac{S_2-S_1}{S_1}}=100\cdot {\displaystyle \frac{236-184}{184}}={\displaystyle \frac{650}{23}}\mathrm{\%}=28.2609\mathrm{\%} \end{gathered}$$

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