Answer to Question #240127 in Civil and Environmental Engineering for Mr. Lee

Question #240127

A prism with an altitude of 15 cm has an octagonal base inscribed in a square with side 10 cm. Find the volume of the prism.

Expert's answer

Regular ooctagon with 15 cm altitude is inscribed in a 10X10 cm. square.

To find it's side length, square has to be cut, such that all sides of octagon are maximum and equal.

inscribed in square ABCD.

Let"BF = BG = CH = CI = X, so GH = 10 - 2X."

By pythagoras theorem,

"FG = \u221a2X and GH = FG =10 - 2X," therefore,

"\u221a2X = 10 - 2X => X(2+\u221a2) = 10 => X = 10\/(2+\u221a2)"

side of the octagon

"= 10 - 20\/(2+\u221a2) \n(20 + 10\u221a2 - 20)\/(2+\u221a2) = 10\u221a2\/(2+\u221a2" )

Area of regular octagon = 2(1+√2)S^2

Volume of prism =>

"V = 15\u00d72(1+\u221a2)[(10\u221a2\/(2+\u221a2)]^2" "V = (30+30\u221a2)[200\/(6+4\u221a2)]"

"V = 6000(1+\u221a2)\/(6+4\u221a2) = 1242.64 cm^3"

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