Superradiance has been extensively studied in the 1970s and 1980s in the regime of superfluorescence, where a large number of atoms are initially excited. Cooperative scattering in the linear-optics regime, or "single-photon superradiance," has been investigated much more recently, and superradiant decay has also been predicted, even for a spherical sample of large extent and low density, where the distance between atoms is much larger than the wavelength. Here, we demonstrate this effect experimentally by directly measuring the decay rate of the off-axis fluorescence of a large and dilute cloud of cold rubidium atoms after the sudden switch off of a low-intensity laser driving the atomic transition. We show that, at large detuning, the decay rate increases with the on-resonance optical depth. In contrast to forward scattering, the superradiant decay of off-axis fluorescence is suppressed near resonance due to attenuation and multiple-scattering effects.