Question

When the length of each edge of a cube is increased by 1 cm, the volume is increased by 19 cm3.A cube is shown.The length is labeled e.The width is labeled e.The height is labeled e.What is the length (in centimeters) of each edge of the original cube? cm

Answer 1

solution given;

let length be x

its

volume be x ³

we have when length is increased by 1cm volume increased by 19 cm³ so

(x+1)³=x³+19cm³

x³+1³+3x²+3x=x³+19

3x²+3x-18=0

3(x²+x-6)=0

x²+3x-2x-6=0

x(x+3)-2(x+3)=0

(x+3)(x-2)=0

either

x=-3 rejected

or

x=2cm

Hence the correct answer for the length of each cube = 2cm