Which hand-scaling instrument is described as having a rounded working end and is used sub-gingivally?

The correct instrument described in the question is the curette. A curette is specifically designed with a rounded working end, which allows for effective and gentle cleaning beneath the gum line, making it ideal for sub-gingival scaling. The rounded design helps to minimize trauma to the surrounding tissue while effectively removing plaque and calculus from the tooth surface and root areas under the gums.

In contrast, a sickle scaler typically has a pointed working end and is better suited for supragingival scaling, where access to the visible areas above the gumline is required. A hoe scaler has a angled blade that is more effective for scrapping debris from tooth surfaces but is not designed for use below the gumline. An explorer, while a useful diagnostic tool for checking the condition of teeth and detecting cavities, does not have the appropriate design for scaling sub-gingivally. Therefore, the curette is the most suitable choice for the task described.