The edge of one cube is 4 m shorter than the edge of a second cube. The volumes of the two cubes differ by 1216 m^3. Find the ed ge of the smaller cube.
2 answers:
Volume of cube, V = edge^3 Let edge of cube#1 = (x-4) m, therefore volume of cube#1, v1 = (x-4)^3 m Let edge of cube#2 = x m, therefore volume of cube#2, v2 = x^3 m Diff. in volume (in m) = 1216 = v2-v1 = [ x^3 - (x-4)^3 ] = x^3 - [(x-4)(x-4)(x-4)] = x^3 - [<span>x^2 - 8x +16(x - 4)] = </span> x^3 - [ x^3 - 12x^2 + 48x - 64 ] = 12x^2 - 48x + 64 = 4 (3x^2 - 12x + 16) Therefore 4 (3^2 - 12x + 16) = 1216 3x^2 - 12x + 16 = 1216/4 = 304 3x^2 - 12x - 288 = 0 3 (x^2 - 4x - 96) = 0 (x^2 - 4x - 96) = 0 (x - 12) (x + 8) =0 (x-12) = 0 Therefore x = 12 m Edge of cube#2 = x m = 12m Edge of cube#1 = (x-4) m = 8m
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