Quadrilateral prism

The surface of the regular quadrilateral prism is 8800 cm2, the base edge is 20 cm long. Calculate the volume of the prism

Correct result:

V =  40000 cm3

Solution:

S=8800 cm2 a=20 cm  S1=a2=202=400 cm2  S=2⋅ S1+4⋅ a⋅ c  c=S−2⋅ S14⋅ a=8800−2⋅ 4004⋅ 20=100 cm  V=S1⋅ c=400⋅ 100=40000 cm3S=8800 \ \text{cm}^2 \ \\ a=20 \ \text{cm} \ \\ \ \\ S_{1}=a^2=20^2=400 \ \text{cm}^2 \ \\ \ \\ S=2 \cdot \ S_{1} + 4 \cdot \ a \cdot \ c \ \\ \ \\ c=\dfrac{ S - 2 \cdot \ S_{1} }{ 4 \cdot \ a }=\dfrac{ 8800 - 2 \cdot \ 400 }{ 4 \cdot \ 20 }=100 \ \text{cm} \ \\ \ \\ V=S_{1} \cdot \ c=400 \cdot \ 100=40000 \ \text{cm}^3

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