Water Tank Capacity?

📌 CONCEPT: The problem involves finding the time taken to fill a portion of a cylinder with water, which can be solved using the concept of volumes of solids and rates of change.

📐 RULE / FORMULA: The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height. To find the time taken to fill the tank, we can use the formula V = rate × time, where the rate is the volume of water being pumped into the tank per unit time.

💡 WORKED EXAMPLE: Let's consider a water tank with height 10 m and base radius 4 m. If water is being pumped into the tank at a rate of 2 m^3/min, we want to find the time taken to fill the tank to a depth of 6 m. First, we find the volume of water needed to fill the tank to a depth of 6 m using the formula V = πr^2h. Then, we use the formula V = rate × time to find the time taken.

⚠️ COMMON MISTAKE: Students often forget to consider the portion of the cylinder that needs to be filled, and instead use the full volume of the cylinder. This can lead to incorrect answers.