Question

A cubed-shaped box has its side lengths decreased by 3 cm, when this happens, the volume decreases by 1385cm^3. What is the side length of the original box?

Answer 1

Explanation:

let side of cube=x cm

volume=x³ cm³

again side=(x-3) cm

volume=(x-3)³ cm³

x³-(x-3)³=1385

(a³-b³)=(a-b)(a²+ab+b²)

(x-x+3){x²+x(x-3)+(x-3)²}=1385

3(x^2+x²-3x+x²-6x+9)=1385

3(3x²-9x+9)=1385

9x²-27x+27=1385

9x²-27x+27-1385=0

9x²-27x-1358=0

`x=(27\pm√((-27)^2-4*9*(-1358)) )/(2*9) \\x=(27\pm√(729+48888) )/(18) \\or~x=(27\pm√(49617) )/(18) \\or~x=(27\pm 222.749)/(18) \\taking positive side only as negative sign gives negative length.\\or~x=(27+222.749)/(18) \\or~x\approx13.87`