The water of for a industry is stored in a hemispherical tank of internal diameter 14 m . The tank contains 40 kilolitres of water. Water is pumped into the tank to fill it to full capacity. Calculate the volume of water pumped into te tank.

To solve the problem, we need to follow these steps: 1. **Extract known conditions:** - The internal diameter of the hemispherical tank is 14 m. - The tank currently contains 40 kilolitres of water. - We need to calculate the volume of water pumped into the tank to fill it to full capacity. 2. **Calculate the volume of the hemispherical tank:** The formula for the volume \( V \) of a hemisphere is given by: \[ V = \frac{2}{3} \pi r^3 \] where \( r \) is the radius of the hemisphere. Since the diameter is 14 m, the radius \( r \) will be: \[ r = \frac{14}{2} = 7 \text{ m} \] 3. **Calculate the volume of the tank:** Now we can substitute the radius into the volume formula: \[ V = \frac{2}{3} \pi (7)^3 \] 4. **Convert the volume of water currently in the tank from kilolitres to cubic meters:** Since 1 kilolitre is equal to 1 cubic meter, 40 kilolitres is: \[ 40 \text{ m}^3 \] 5. **Calculate the volume of water pumped into the tank:** The volume of water to be pumped is the difference between the full volume of the tank and the current volume of water. Now, let's perform the calculations step by step. First, we will calculate the volume of the tank. Calculate the value by following steps: - step0: Calculate: \(\frac{2}{3}\pi \times 7^{3}\) - step1: Multiply: \(\frac{2\pi }{3}\times 7^{3}\) - step2: Multiply: \(\frac{2\pi \times 7^{3}}{3}\) - step3: Multiply: \(\frac{686\pi }{3}\) Calculate or simplify the expression \( 718.37752 - 40 \). Calculate the value by following steps: - step0: Calculate: \(718.37752-40\) - step1: Subtract the numbers: \(678.37752\) 1. **Volume of the hemispherical tank:** The volume of the tank is approximately \( 718.38 \, \text{m}^3 \). 2. **Current volume of water in the tank:** The tank currently contains \( 40 \, \text{m}^3 \) of water. 3. **Volume of water to be pumped into the tank:** The volume of water that needs to be pumped into the tank is: \[ 718.38 \, \text{m}^3 - 40 \, \text{m}^3 = 678.38 \, \text{m}^3 \] Thus, the volume of water pumped into the tank is approximately **678.38 cubic meters**.