Question

If each side of a cube is increased by 2 cm, the volume increases by 488 cm³. Find the side of the cube.

Answer 1

We have,

If each side of a cube is increased by 2 cm, the volume increases by 488 cm³.

Now we know that,

Volume of a cube is (Edge)³

Let the length of the edge of the cube be x cm

Then, length after 2 cm increase is (x + 2) cm

Now, the original volume of the cube is (x)³ cm³

And the volume of the new cube is (x + 2)³ cm³

According to the question,

(x + 2)³ – (x)³ = 488

x³ + 2³ + 6x² + 12x – x³ = 488  ...[Using a + b³ = a³ + b³ + 3a²b + 3ab²]

6x² + 12x – 480 = 0

x² + 2x – 80 = 0

x² + 10x – 8x – 80 = 0

x(x + 10) – 8(x + 10) = 0

(x + 10)(x – 8) = 0

x = –10 cm or x = 8 cm

As sides of the cube can not be in negative

Therefore, the side of the cube is 8 cm.