Prism bases

Volume perpendicular quadrilateral prism is 360 cm³. The edges of the base and height of the prism are in the ratio 5:4:2 Determine the area of the base and walls of the prism.

Result

S₁ =  86.535 cm²
S₂ =  34.614 cm²
S₃ =  43.267 cm²

Solution:

$V=360 \ \\ a:b:c=5:4:2 \ \\ V=abc=5 \cdot \ 4 \cdot \ 2 \cdot \ k^3 \ \\ k=\sqrt[3]{ V/(5 \cdot \ 4 \cdot \ 2)}=\sqrt[3]{ 360/(5 \cdot \ 4 \cdot \ 2)} \doteq 2.0801 \ \\ a=5 \cdot \ k=5 \cdot \ 2.0801 \doteq 10.4004 \ \\ b=4 \cdot \ k=4 \cdot \ 2.0801 \doteq 8.3203 \ \\ c=2 \cdot \ k=2 \cdot \ 2.0801 \doteq 4.1602 \ \\ S_{1}=a \cdot \ b=10.4004 \cdot \ 8.3203 \doteq 86.535 \doteq 86.535 \ \text{cm}^2$

$S_{2}=b \cdot \ c=8.3203 \cdot \ 4.1602 \doteq 34.614 \doteq 34.614 \ \text{cm}^2$

$S_{3}=c \cdot \ a=4.1602 \cdot \ 10.4004 \doteq 43.2675 \doteq 43.267 \ \text{cm}^2$

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