If the volume of the solid shown in the figure s 504 cubic i

If the volume of the solid shown in the figure s 504 cubic inches, find the value of x.

There are 3 cuboids in the figure,

the two cuboids on left and rifght side have dimesions = x+5 , (2x +3 -x)/2 , 3

The cuboid as the base has dimensions = 2x+3 , x+5 , x+2

So, total volume = sum of volumes of 3 cuboids

= (x+5)(x +3)/2(3) +(x+5)(x +3)/2(3) + (2x +3)(x+5)(x+2)

= (x+5)(x +3)(3) +(2x +3)(x+5)(x+2)

= 3(x^2 +8x+15) + (2x^2 +10x +3x +15)(x+2)

= 3x^2 +24x +45 + 2x^3 +4x^2 13x^2 +26x +15x +30

= 2x^3 + 7x^2+ 50x + 75

2x^3 + 7x^2+ 50x + 75 = 504

2x^3 + 7x^2+ 50x - 429 =0

solve the cubic equation for x:

x = 3.94 ; x = -3.72 +i6.36

Neglect the complex roots:

x = 3.94 iches