The height of a right prism with a square bas | vedclass

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Question

(C) Let the side of the square base be $x\, cm.$ The height of the prism is $h = 15\, cm.$ The total surface area of a prism is given by the formula:

Vedclass · Accepted Answer

$960$

Vedclass · Answer

(C) Let the side of the square base be $x\, cm.$ The height of the prism is $h = 15\, cm.$ The total surface area of a prism is given by the formula: $	ext{Total Surface Area} = 	ext{Lateral Surface Area} + 2 	imes 	ext{Base Area}.$ Lateral Surface Area $= 	ext{Perimeter of base} 	imes h = (4x) 	imes 15 = 60x.$ Base Area $= x^2.$ Given,$	ext{Total Surface Area} = 608\, cm^2.$ So,$60x + 2x^2 = 608.$ Dividing by $2,$ we get $x^2 + 30x - 304 = 0.$ Factoring the quadratic equation: $x^2 + 38x - 8x - 304 = 0 \Rightarrow x(x + 38) - 8(x + 38) = 0.$ $(x - 8)(x + 38) = 0.$ Since the side length cannot be negative,$x = 8\, cm.$ Volume of the prism $= 	ext{Base Area} 	imes h = x^2 	imes h = 8^2 	imes 15 = 64 	imes 15 = 960\, cm^3.$

The height of a right prism with a square base is $15\, cm.$ If the total surface area of the prism is $608\, cm^2,$ its volume is......$cm^3$.

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