If the edge of a cube is increased by 2 cm, the volume will increase by 488 cm$$^3$$. What then will be the length of each edge of the cube?
Let the length of the cube be x
Length after 2cm increase = x + 2
Find the original volume:
Volume = Length³
Volume = x³
Find the new volume:
Volume = Length³
Volume = (x + 2)³
Form equation and solve for x:
The volume is increased by 488 cm
(x + 2)³ - x³ = 488
x³ +6x² +12x + 8 - x³ = 488
6x² +12x - 480 = 0
x² +2x - 80 = 0
(x - 8)(x + 10) = 0
x = 8 or x = - 10 (rejected, x cannot be negative)
length:8
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