SYDNEY—Australia’s biggest city has been shrouded in hazardous smoke for the past week, as wildfires burning across the country’s drought-stricken east coast are—in some cases—becoming too big to put out.

The fires are turning the daytime sky in Sydney orange and causing air quality to dip to levels more often seen in cities like Delhi and Beijing. Schools are keeping students inside during recess and canceling sports and other outdoor activities.

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