Lesson 6.4: Help for Exercise 88 on page 349
Start by creating a verbal model of the situation. To find the outside dimensions of the tank, you need to know the total volume of the tank. To find this you can add the volume of steel to the volume of the interior, which are given to you.
After finding the total volume you can use the solution to find the dimensions of the tank. Use the formula for volume of a rectangular solid, V = lwh. The dimensions are represented by the expressions x, (x + 1), and (x + 10). Assign labels from the information given and write an algebraic model. The algebraic expression for the total volume can be found by substituting the dimensions of the tank into the formula for volume of a rectangular solid. Your algebraic model will be a polynomial with a degree of three. Solve this polynomial for zero. Because conventional factoring techniques do not apply to this problem, you need to test different values of x until you find a value that makes the polynomial equation equal zero. Try factors of the total volume; one of these factors will provide the correct answer.