Question 56

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?

Solution

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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