Final answer:
To calculate how fast the water level in a rectangular pool is rising when being filled by a garden hose, divide the volume of water added per minute (0.1 m³) by the pool's base area (32 m²), resulting in a rise of 3.125 mm per minute.
Step-by-step explanation:
The question is asking to find out how fast the water level is rising in a rectangular pool that is being filled with water. To solve this problem, we need to find the volume of the pool and then calculate the rate at which the volume is increasing with the water being added by the garden hose.
The pool dimensions are 4 meters wide, 8 meters long, and we don't know the depth (height) yet. Since the volume of water coming from the hose is 1 cubic meter every 10 minutes, this means that every minute, 0.1 cubic meters of water is added to the pool.
To find out how fast the water level is rising, we divide the volume added per minute by the area of the base of the pool:
- Volume added per minute = 0.1 cubic meters
- Area of the pool's base = Width × Length = 4 m × 8 m = 32 m²
- Rise in water level per minute = Volume added per minute ÷ Area of the pool's base
- Rise in water level per minute = 0.1 m³/min ÷ 32 m² = 0.003125 m/min or 3.125 mm/min
Therefore, the water is rising at a rate of 3.125 mm per minute.