A village wishes to measure the quantity of water that is piped to a factory during a typical morning. A gauge on the water line gives the flow rate (in cubic meters per hour) at any instant. The flow rate is about 90m³ /hr. at 6 am and increases steadily to about 280m³ / hr. at 9 am. Using only this information, give your best estimate of the total volume of water used by the factory between 6 am and 9 am.

Best estimate = __________________m³