Which PromQL expression computes the rate of API Server requests across the different cloud providers...

Therate()function computes theper-second increaseof a counter metric over a specified range, whilesum by (label)aggregates those rates across dimensions — in this case, the cloud label.

The correct query is:

sum by (cloud)(rate(apiserver_request_total{job="kube-apiserver"}[5m]))

This expression:

Calculates the rate of increase in API requests per second for each instance.

Groups and sums those rates by cloud, giving the total request rate per cloud provider.

Option A incorrectly places by (cloud) after rate(), which is not valid syntax.

Option B returns raw counter totals (not rates).

Option D incorrectly applies rate() after aggregation, which distorts the calculation since rate() must operate on individual time series before aggregation.