Answer :
Certainly! Let's solve this step-by-step:
1. Initial Information:
- The side of the square base of the tank is 15 cm.
- The initial volume of water in the tank is 4.05 liters.
- An additional 2.25 liters of water is added to the tank.
2. Total Volume of Water:
- The volume of water initially in the tank = 4.05 liters.
- The volume of water added to the tank = 2.25 liters.
- Total volume of water in the tank = 4.05 liters + 2.25 liters = 6.3 liters.
3. Convert Volume to Cubic Centimeters:
- Since 1 liter = 1000 cubic centimeters (cm³), we need to convert the total volume from liters to cubic centimeters.
- Total volume = 6.3 liters × 1000 cm³/liter = 6300 cm³.
4. Calculate Area of the Square Base:
- The side of the square base = 15 cm.
- Area of the square base = side × side = 15 cm × 15 cm = 225 cm².
5. Calculate the Height of the Tank:
- We know the volume of a rectangular tank is given by the formula:
[tex]\[ \text{Volume} = \text{Base Area} \times \text{Height} \][/tex]
- Rearranging for height, we get:
[tex]\[ \text{Height} = \frac{\text{Volume}}{\text{Base Area}} \][/tex]
- Substitute the known values into the formula:
[tex]\[ \text{Height} = \frac{6300 \text{ cm}³}{225 \text{ cm}²} \][/tex]
- Solving this, we get:
[tex]\[ \text{Height} = 28 \text{ cm} \][/tex]
So, the height of the tank is 28 cm.
1. Initial Information:
- The side of the square base of the tank is 15 cm.
- The initial volume of water in the tank is 4.05 liters.
- An additional 2.25 liters of water is added to the tank.
2. Total Volume of Water:
- The volume of water initially in the tank = 4.05 liters.
- The volume of water added to the tank = 2.25 liters.
- Total volume of water in the tank = 4.05 liters + 2.25 liters = 6.3 liters.
3. Convert Volume to Cubic Centimeters:
- Since 1 liter = 1000 cubic centimeters (cm³), we need to convert the total volume from liters to cubic centimeters.
- Total volume = 6.3 liters × 1000 cm³/liter = 6300 cm³.
4. Calculate Area of the Square Base:
- The side of the square base = 15 cm.
- Area of the square base = side × side = 15 cm × 15 cm = 225 cm².
5. Calculate the Height of the Tank:
- We know the volume of a rectangular tank is given by the formula:
[tex]\[ \text{Volume} = \text{Base Area} \times \text{Height} \][/tex]
- Rearranging for height, we get:
[tex]\[ \text{Height} = \frac{\text{Volume}}{\text{Base Area}} \][/tex]
- Substitute the known values into the formula:
[tex]\[ \text{Height} = \frac{6300 \text{ cm}³}{225 \text{ cm}²} \][/tex]
- Solving this, we get:
[tex]\[ \text{Height} = 28 \text{ cm} \][/tex]
So, the height of the tank is 28 cm.
