The in-vivo investigation of highly dynamic biological samples, for example the beating zebrafish heart, requires high-speed volume imaging techniques. Light-sheet microscopy is ideal for such samples as it records high-contrast images of entire planes within large samples at once. However, in order to obtain images of different planes, it has been necessary to move the sample relative to the fixed focal plane of the detection objective lens. This mechanical movement limits speed, precision and may be harmful to the sample. We have built a light-sheet microscope that uses remote focusing with an electrically tunable lens (ETL). Without moving specimen or objective we have thereby achieved flexible volume imaging at much higher speeds than previously reported. Our high-speed microscope delivers 3D snapshots of sensitive biological samples. As an example, we imaged 17 planes within a beating zebrafish heart at 510 frames per second, equivalent to 30 volume scans per second. Movements, shape changes and signals across the entire volume can be followed which has been impossible with existing reconstruction techniques.