A right prism has square bases with edges that are three times as long as the lateral edges. The prism's total area is 750 m squared. Find the volume.

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25-05-2014
Mathematics

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A right prism has square bases with edges that are three times as long as the lateral edges. The prism's total area is 750 m squared. Find the volume.

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Kate200468idn Kate200468idn · Answer 1 · 2014-05-25T15:30:14-04:00

Kate200468idn Kate200468idn

25-05-2014

[tex]a=3h\ \ \ and\ \ \ A=2\cdot a^2+4\cdot a\cdot h\\\\A=2\cdot(3h)^3+4\cdot 3h\cdot h=2\cdot 9h^2+12h^2=30h^2\\\\A=750\ m^2\\\\\ \ \ \Rightarrow\ \ \ 30h^2=750\ /:30\ \ \ \Rightarrow\ \ \ h^2=25\ \ \ \Rightarrow\ \ \ h=5\ \ \ \Rightarrow\ \ \ a=15\\\\V=a^2\cdot h=15^2\cdot 5=225\cdot 5=1125\\\\Ans.\ Volume=1125\ m^3.[/tex]

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