Question

if the edge of a cube is increased by 2 cm, the volume will increase by 488cm cube. then what will be the length of each edge of cube?

Answer 1

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)

Find the new length:

New length = 8 + 2 = 10 cm

Answer: The new length is 10 cm

Answer 2

Answer:

Step-by-step explanation:

Let the original cube's edge = x

Volume = x^3

New edge = (x+2)

(x+2)^3 = x^3 + 488

x^3 + 8 +6x^2 + 12x = x^3 + 488

6x^2 + 12x -480 = 0

Dividing the equation by 6,

x^2 + 2x - 80 = 0

(x+10) (x-8) = 0

The length of the each edge is 8 cm