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.

Correct result:

S₁ =  86.535 cm²
S₂ =  34.614 cm²
S₃ =  43.2675 cm²

Solution:

$$\begin{gathered} V=360 \\ a:b:c=5:4:2 \\ V=abc=5\cdot 4\cdot 2\cdot k^3 \\ k=\sqrt[3]{V\mathrm{/}(5\cdot 4\cdot 2)}=\sqrt[3]{360\mathrm{/}(5\cdot 4\cdot 2)}\doteq 2.0801 \\ a=5\cdot k=5\cdot 2.0801\doteq 10.4004 \\ b=4\cdot k=4\cdot 2.0801\doteq 8.3203 \\ c=2\cdot k=2\cdot 2.0801\doteq 4.1602 \\ {S}_1=a\cdot b=10.4004\cdot 8.3203=86.535{\text{cm}}^2 \end{gathered}$$

$S_2=b\cdot c=8.3203\cdot 4.1602=34.614{\text{cm}}^2$

$S_3=c\cdot a=4.1602\cdot 10.4004=43.2675{\text{cm}}^2$

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