1. **State the problem:** We need to find the total volume of a solid made by joining a cylinder and a hemisphere, both having radius $1.5$ cm. The cylinder's height is $4$ cm. 2. **Formulas used:** - Volume of a cylinder: $$V_{cyl} = \pi r^2 h$$ - Volume of a hemisphere: $$V_{hem} = \frac{2}{3} \pi r^3$$ 3. **Calculate the volume of the cylinder:** $$V_{cyl} = \pi \times (1.5)^2 \times 4 = \pi \times 2.25 \times 4 = 9\pi$$ 4. **Calculate the volume of the hemisphere:** $$V_{hem} = \frac{2}{3} \pi \times (1.5)^3 = \frac{2}{3} \pi \times 3.375 = 2.25\pi$$ 5. **Calculate the total volume:** $$V_{total} = V_{cyl} + V_{hem} = 9\pi + 2.25\pi = 11.25\pi$$ 6. **Evaluate the numerical value:** $$V_{total} = 11.25 \times 3.1416 = 35.3427...$$ 7. **Round to 3 significant figures:** $$\boxed{35.3 \text{ cm}^3}$$ This is the total volume of the solid.