Question

A rectangilar safe is to be made of steel of uniform thickness, including the door the inside dimensions are 1.20 m ,1.20 m and 2.00 m if the volume of the steel is 1.25m^3 find its thickness

Answer 1

The INSIDE dimensions of the rectangular safe :
Length L = 1.20 m        Breadth B = 1.20 m          Height H = 2.00 m
Let thickness of safe be t meters

To get the outside dimensions: add t on each side of a dimension.( left side and right side for widht and length. Also at top and bottom for height).  so each dimension becomes plus 2t. 

Outside Length = 1.20+2t     width  = 1.20+2t    height = 2.00+2t
Ouside volume = (1.2+2t)² (2+2t)  = 2²(0.6+t)² 2 (1+t)

The volume of Steel used is the difference of the outside volume and inside volume.

Hence :  8(t²+1.2t+0.6²)(1+t) - 1.2² * 2 = 1.25 meter³

  8 (t² + 1.2 t + 0.36 + t³ + 1.2t² + 0.36 t) - 2.88 = 1.25

  8 t³ + 17.6 t² + 12.48 t + 2.88 - 2.88 = 1.25

find t by solving the equation.  The roots of this polynomial could be possibly
           factors of   +-  1.25  / factors of 8

t = 0.0886 meters  or 0.0887   meter    ,       that is 8.86 cm or 0.0887 cm approx.

t is so small that t³ is very small compared to t² and t.  SO neglect the t³ term and solve the equation using te quadratic equation formula. The answer u get will be very close the actual one.