Final answer:
The surface area of an open-ended cylinder is given by S = 2πrh. Damien can paint a tunnel that is approximately 0.96 meters long with his 30 square meters of paint.
Step-by-step explanation:
The formula for the surface area of a cylinder open at both ends is S = 2πrh, where 'r' is the radius and 'h' is the height (or length) of the cylinder. Since Damien has enough red paint to cover an area of 30 square meters and the radius of the playground tunnel is 5 meters, we can solve for the length (h) of the tunnel he can paint using this formula: 30 m² = 2π(5 m)h. Simplifying the equation yields: h = 30 m² / (2π×5 m), or h = 30 / (10π), which gives h = 3 / π. For π approximately equal to 3.14, this becomes h = 3 / 3.14, and thus h ≈ 0.955 meters, which rounds to 0.96 meters.