Problema Solution
Consider a cube. Let the length of its each edge be x meters, so the volume of the cube is x3. Let the increase in volume be 98 m3 when the edge is increased by 3 meters. Find the original length of each side of the cube?
Answer provided by our tutors
original volume: x^3 = V
new volume: (x+3)^3 = V + 98
subtract these equations:
(x+3)^3 - x^3 = 98
(x^2 + 6x + 9)(x+3) - x^3 = 98
(x^3 + 3x^2 + 6x^2 + 18x + 9x + 27) - x^3 = 98
x^3 + 9x^2 + 27x + 27 - x^3 = 98
9x^2 + 27x + 27 = 98
factorise using scientific calculator
x1=1.6841622 , x2=-4.6841622
hence, x= 1.684