#### To determine

**To find:**

The depth of the water remaining in the tank

#### Answer

h=2.028 m

#### Explanation

**1) Concept:**

The work is calculated by using the formula W=∫abf(x)dx

**2) Given:**

4.7×105 J of work is done

**3) Calculation:**

If 4.7×105 J of work is done, then the water above a certain level will be pumped out.

Therefore, use the same formula as in exercise 23 except that the work is fixed and find the lower limit of integration:

4.7×105≈∫h39.8×1035-x8x dx

=9.8×103∫h35-x8x dx

=9.8×103∫h340x-8x2 dx

=9.8×10340x22-8x33h3

=9.8×10340·322-8·333-40·h22-8·h33

4.7×105=9.8×10340·92-8·273-40·h22-8·h33

Simplifying this

2h3-15h2+45=0

To solve this equation plot a graph between h=0 and h=3

Therefore, at value of h=2.028(between 0 and 3) the equation is zero.

Therefore the depth of the water remaining in the tank is h=2.028 m

**Conclusion:**

The depth of the water remaining in the tank is h=2.028 m