To determine which fish tank holds more water, we need to calculate the volume of each tank using the appropriate formulas.
1. Calculate the Volume
A. Volume of the Rectangular Prism Tank
The formula for the volume \( V \) of a rectangular prism is: \[ V = \text{length} \times \text{width} \times \text{height} \]
Given:
- Length = 30 cm
- Width = 20 cm
- Height = 50 cm
Now substitute the values into the formula: \[ V = 30 , \text{cm} \times 20 , \text{cm} \times 50 , \text{cm} \]
Calculating: \[ V = 30 \times 20 = 600 , \text{cm}^2 \] \[ V = 600 , \text{cm}^2 \times 50 , \text{cm} = 30000 , \text{cm}^3 \]
Thus, the volume of the rectangular prism tank is 30,000 cm³.
B. Volume of the Cylindrical Tank
The formula for the volume \( V \) of a cylinder is: \[ V = \pi r^2 h \]
Given:
- Radius \( r = 15 , \text{cm} \)
- Height \( h = 50 , \text{cm} \)
Now substitute the values into the formula: \[ V = \pi (15 , \text{cm})^2 (50 , \text{cm}) \] Calculating \( (15 , \text{cm})^2 \): \[ (15 , \text{cm})^2 = 225 , \text{cm}^2 \]
Now substitute: \[ V = \pi \times 225 , \text{cm}^2 \times 50 , \text{cm} \] \[ V = \pi \times 11250 , \text{cm}^3 \]
Using \( \pi \approx 3.14 \): \[ V \approx 3.14 \times 11250 , \text{cm}^3 \approx 35325 , \text{cm}^3 \]
Thus, the volume of the cylindrical tank is approximately 35,325 cm³.
2. Compare the Volumes
Now we will compare the volumes of both tanks:
- Rectangular Prism Volume: 30,000 cm³
- Cylindrical Tank Volume: 35,325 cm³
3. Conclusion
The cylindrical tank has a greater volume of approximately 35,325 cm³, compared to the rectangular prism tank which holds 30,000 cm³.
4. Bigger Fish Tank
Based on the calculations, the cylindrical tank should hold the bigger fish since it has a greater volume.