Final answer:
The surface charge density of the balloon is roughly 7.957 × 10^-3 C/m^2 when calculated with the given radius and charge.
Step-by-step explanation:
To estimate the surface charge density of a round balloon with radius r = 0.1 m and an electric charge Q = 0.001 C distributed evenly over its surface, we use the formula for the surface area of a sphere and the definition of surface charge density, which is charge per area.
The surface area A of a sphere can be calculated using the equation A = 4πr^2. Plugging in the radius r of the balloon, we get A = 4π(0.1 m)^2 which equals 0.04π m^2.
The surface charge density σ is given by σ = Q/A. Using Q = 0.001 C and A = 0.04π m^2, we find σ = (0.001 C) / (0.04π m^2), which roughly equals 7.957 × 10^-3 C/m^2 when rounded to three decimal places.