Select the correct answerA cube's volume increases by 728 cm³ when the length of each side is increased by 2 cm. Find the original length of a side.Options7 cm11 cm8 cm10 cm

The volume of a cube is given by the formula V = s³, where s is the length of a side.

When the length of each side is increased by 2 cm, the volume becomes (s+2)³.

According to the problem, the difference in the volumes is 728 cm³.

So, we have the equation (s+2)³ - s³ = 728.

Expanding and simplifying, we get 6s² + 12s + 8 = 728.

Subtracting 728 from both sides, we get 6s² + 12s - 720 = 0.

Dividing the entire equation by 6, we get s² + 2s - 120 = 0.

This is a quadratic equation in the form ax² + bx + c = 0.

The solutions of this equation can be found using the quadratic formula s = [-b ± sqrt(b² - 4ac)] / (2a).

Substituting the values a = 1, b = 2, and c = -120 into the formula, we get s = [-2 ± sqrt((2)² - 41(-120))] / (2*1).

Solving this, we get s = -2 ± sqrt(4 + 480) / 2 = -2 ± sqrt(484) / 2 = -2 ± 22 / 2.

The two possible solutions are s = 10 and s = -12.

Since the length of a side cannot be negative, the original length of a side of the cube is 10 cm.

So, the correct answer is 10 cm.