Question 7

# If the edge of a cube is increased by 3 $$cm$$,the volume will increase by 657 $$cm^3$$. What then is the original length of each edge of the cube?

Solution

Let the length of the cube be x

Length after 3cm increase = x + 3

Find the original volume:

Volume =$$Length^3$$

Volume = $$x^3$$

Find the new volume:

Volume = $$Length^3$$

Volume = $$(x + 3)^3$$

Form equation and solve for x:

The volume is increased by 657 cm

$$(x + 3)^3 - x^3 = 657$$

$$x^3 +9x² +27x + 27- x^3 = 657$$

$$9x^2 +27x - 630$$ = 0

$$x^2 +3x - 70$$= 0

(x - 7)(x + 10) = 0

x = 7 or x = - 10 (rejected, x cannot be negative)

Find the new length:

New length = 7 + 3 = 10 cm