1. **State the problem:** We need to find the force exerted by the prism on the floor given the pressure and the volume of the prism. 2. **Identify given information:** - Height of prism, $h = 3$ m - Volume of prism, $V = 18$ m$^3$ - Pressure on floor, $P = 75$ newtons/m$^2$ 3. **Recall the formula for pressure:** $$P = \frac{F}{A}$$ where $F$ is the force and $A$ is the area of contact with the floor. 4. **Find the area of the base of the prism:** Since volume $V = A \times h$, we have $$A = \frac{V}{h} = \frac{18}{3} = 6 \text{ m}^2$$ 5. **Calculate the force:** Rearranging the pressure formula, $$F = P \times A = 75 \times 6 = 450 \text{ newtons}$$ **Final answer:** The force exerted by the prism on the floor is **450 newtons**.