Question 9

If the edge of a cube is increased by 4 cm, the volume will increase by 988$$cm^3$$. Then the original length of each edge of the cube is

Solution

Let x be the original size of the cube.

If the edge of a cube is increased by 4 cm, the volume will increase by 988$$cm^3$$.

According to question,

$$(x+4)^3-x^3=988$$

$$x^3+12x^2+48x+64-x^3 = 988$$

$$12x^2+48x=988-64$$

$$12x^2+48x-924=0$$

$$x^2+4x-77=0$$

$$x=-11,7$$

x = 7 cm

Option A is correct.