1. **State the problem:** We need to find the pressure exerted on the floor by a solid cylinder. 2. **Given data:** - Volume of cylinder $V = 1200$ cm$^3$ - Height of cylinder $h = 40$ cm - Force exerted $F = 90$ newtons 3. **Formula for pressure:** $$\text{Pressure} = \frac{\text{Force}}{\text{Area}}$$ 4. **Find the area of the base of the cylinder:** The base is a circle, so area $A = \pi r^2$. 5. **Find the radius $r$ using the volume formula for a cylinder:** $$V = \pi r^2 h$$ Rearranged to find $r^2$: $$r^2 = \frac{V}{\pi h}$$ Substitute values: $$r^2 = \frac{1200}{\pi \times 40} = \frac{1200}{40\pi} = \frac{30}{\pi}$$ 6. **Calculate the area $A$:** $$A = \pi r^2 = \pi \times \frac{30}{\pi} = 30 \text{ cm}^2$$ 7. **Calculate the pressure:** $$\text{Pressure} = \frac{F}{A} = \frac{90}{30} = 3 \text{ newtons/cm}^2$$ **Final answer:** The pressure exerted on the floor is $3$ newtons per cm$^2$.