1. **State the problem:** We have two cylinders, A and B. Cylinder A has radius $3.5$ cm and height $7.4$ cm and is $40\%$ full of liquid. The liquid is poured into cylinder B, which has radius $6.9$ cm and height $3.5$ cm. We need to find the percentage of cylinder B that is filled with this liquid. 2. **Formula for volume of a cylinder:** The volume $V$ of a cylinder is given by: $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Calculate the volume of liquid in cylinder A:** First, find the total volume of cylinder A: $$V_A = \pi \times (3.5)^2 \times 7.4 = \pi \times 12.25 \times 7.4$$ $$V_A = \pi \times 90.65 = 90.65\pi$$ Since cylinder A is $40\%$ full, the volume of liquid is: $$V_{liquid} = 0.40 \times 90.65\pi = 36.26\pi$$ 4. **Calculate the total volume of cylinder B:** $$V_B = \pi \times (6.9)^2 \times 3.5 = \pi \times 47.61 \times 3.5$$ $$V_B = \pi \times 166.635 = 166.635\pi$$ 5. **Find the fraction of cylinder B filled by the liquid:** $$\text{Fraction filled} = \frac{V_{liquid}}{V_B} = \frac{36.26\pi}{166.635\pi} = \frac{36.26}{166.635}$$ Canceling $\pi$: $$\frac{36.26\cancel{\pi}}{166.635\cancel{\pi}}$$ 6. **Calculate the percentage filled:** $$\text{Percentage filled} = \frac{36.26}{166.635} \times 100 = 21.8\%$$ **Final answer:** Cylinder B is filled to **21.8\%** of its volume.