Chapter 4.5, Problem 55E

To determine

To find: the outer dimensions of the basin be if is to hold 36 cubic feet of water.

Answer to Problem 55E

The outer dimension of basin is $\text{8ft×4ft×4ft}$ .

Explanation of Solution

Given information:

The sides and bottom of the basin should be 1 foot thick. Its outer length should be twice its outer width and outer height.

  

Calculation:

The volume is product of length, width and height, so

  $\begin{array}{c}V=\left(2x-2\right)\left(x-1\right)\left(x-2\right)\\ 36=\left(2x-2\right)\left(x^2-3x+2\right)\\ 36=2x^3-8x^2+10x-4\\ x^3-4x^2+5x-20=0\end{array}$

Now solve the equation for $x$

  $\begin{array}{c}\left(x^3-4x^2\right)+\left(5x-20\right)=0\\ x^2\left(x-4\right)+5\left(x-4\right)=0\\ \left(x-4\right)\left(x^2+5\right)=0\\ x=4\left[x^2+5\ne 0\right]\end{array}$

Therefore, the outer dimension of basin is $\text{8ft×4ft×4ft}$ .