Silver nanoparticles coated with silica can be obtained by the reduction of $AgNO_3$ with hydrazine in the presence of NaOH-stabilized, active silicic acid (polysilicic acid). The size of the silver nanoparticles and the silica shell thicknesses were affected by varying the hydrazine content, the active silicic acid content and the experimental method (e.g. hydrothermal method). Typically, silver nanoparticles sized around 40 nm were aggregated, connected by silica. The presence of peaks centered around 400 nm in UV-vis spectra corresponds to the surface plasmon resonance of silver nanoparticles. The size of the aggregated silver nanoparticles increased with increasing hydrazine concentration. Under hydrothermal conditions at $150^{circ}C$ the formation of individual silica particles was observed and the sizes of the silver nanoparticles were reduced. The hydrothermal treatment of silver nanoparticles at $180^{circ}C$ gives a well-defined Ag@$SiO_2$ core-shell in aggregated silica sol particles. The absorption band observed at around 412 nm were red-shifted with respect to the uncoated silver nanoparticles (${lambda}_{max}$ = 399 nm) due to the larger refractive index of silica compared to that of water. The formation of silver nanoparticles coated with silica is confirmed by UV-visible absorption spectra, transmission electron microscopy (TEM) and energy-dispersive spectroscopy (EDS) data.