Question

a tanks in a shape of a rectangular prism has dimensions 2x, 5x 3, and 3x 1 metre . a metal block is dropped into the tank then filled with water. the volume of waters is 22x^3 18x^3 3x cubic meters. determine the dimensions of the metal block?

Answer 1

I have to edit your expressions. If do not guess the right expressions you can do the maths because I will give you the procedure step by step.

1) Dimensions: 2x, 5x + 3, 3x + 1.

2) Volume of water: 22x^3 + 18x^2 + 3x [I changed the exponent of 18x^3 to 18x^2 because I think there was a mistake]

3) Calculations:

Volume of the tank = (2x)(5x+3)(3x+1) = 2x(15x^2+5x+9x+3) = 2x(15x^2+14x+3) =

= 30x^3+28x^2+6x

Volume of water = 22x^3 + 18x^2 + 3x

Volumen of the block = volume of tank - volume of water =(30x^3+28x^2+6x) - ( 22x^3 + 18x^2 + 3x) = 30x^3 +28x^2 +6x -22x^3 -18x^2 -3x =

= 8x^3 + 10x^2 + 3x

Now we can factor this last polynomial:

x(8x^2 + 10x +3) =x(2x+1)(4x+3).

The the dimensions of the metal block are x, 2x+1, 4x+3