1. **State the problem:** We need to find the mass of helium gas required to fill the space between two cylinders: a large cylinder with radius 7 m and height 15 m, and a smaller cylinder inside it with radius 3 m and height 5 m. 2. **Formula and concepts:** The density formula is $\rho = \frac{m}{V}$ where $\rho$ is density, $m$ is mass, and $V$ is volume. We want to find $m = \rho \times V$. 3. **Calculate volumes:** Volume of a cylinder is $V = \pi r^2 h$. - Large cylinder volume: $$V_{large} = \pi \times 7^2 \times 15 = \pi \times 49 \times 15 = 735\pi$$ - Small cylinder volume: $$V_{small} = \pi \times 3^2 \times 5 = \pi \times 9 \times 5 = 45\pi$$ 4. **Calculate volume of helium gas space:** $$V_{helium} = V_{large} - V_{small} = 735\pi - 45\pi = (735 - 45)\pi = 690\pi$$ 5. **Calculate mass of helium gas:** Given density $\rho = 2.7$ kg/m$^3$, $$m = \rho \times V = 2.7 \times 690\pi = 1863\pi$$ 6. **Evaluate numerical value:** Using $\pi \approx 3.1416$, $$m \approx 1863 \times 3.1416 = 5853.6$$ **Final answer:** Approximately 5854 kg of helium gas are required.