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?

Result

p =  28.261 %

Solution:

a=4 cm b=5 cm c=8 cm  a1=2+a=2+4=6 cm  S1=2⋅ (a⋅ b+b⋅ c+c⋅ a)=2⋅ (4⋅ 5+5⋅ 8+8⋅ 4)=184 cm2 S2=2⋅ (a1⋅ b+b⋅ c+c⋅ a1)=2⋅ (6⋅ 5+5⋅ 8+8⋅ 6)=236 cm2  p=100⋅ S2−S1S1=100⋅ 236−184184≐65023≐28.2609≐28.261%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 \ \dfrac{ S_{2}-S_{1} }{ S_{1} }=100 \cdot \ \dfrac{ 236-184 }{ 184 } \doteq \dfrac{ 650 }{ 23 } \doteq 28.2609 \doteq 28.261 \%

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