To determine which fish tank holds more water, we'll calculate the volume of both the rectangular prism and the cylindrical tank using appropriate volume formulas.
Step 1: Calculate the Volume of Each Fish Tank
Volume of the Rectangular Prism Tank
The formula for the volume \( V \) of a rectangular prism is:
\[ V = \text{length} \times \text{width} \times \text{height} \]
For the rectangular prism tank:
- Length = 30 cm
- Width = 20 cm
- Height = 50 cm
Substituting these values into the formula:
\[ V_{\text{rectangular prism}} = 30 , \text{cm} \times 20 , \text{cm} \times 50 , \text{cm} \]
Calculating:
\[ V_{\text{rectangular prism}} = 30 \times 20 = 600 , \text{cm}^2 \]
Now, multiply by the height:
\[ V_{\text{rectangular prism}} = 600 , \text{cm}^2 \times 50 , \text{cm} = 30000 , \text{cm}^3 \]
Volume of the Cylindrical Tank
The formula for the volume \( V \) of a cylinder is:
\[ V = \pi r^2 h \]
Where:
- \( r \) = radius
- \( h \) = height
For the cylindrical tank:
- Radius = 15 cm
- Height = 50 cm
Substituting these values into the formula:
\[ V_{\text{cylinder}} = \pi (15 , \text{cm})^2 (50 , \text{cm}) \]
Calculating \( (15 , \text{cm})^2 \):
\[ (15 , \text{cm})^2 = 225 , \text{cm}^2 \]
Now, substituting back into the volume formula:
\[ V_{\text{cylinder}} = \pi \times 225 , \text{cm}^2 \times 50 , \text{cm} \]
Calculating:
\[ V_{\text{cylinder}} = \pi \times 11250 , \text{cm}^3 \]
Using \( \pi \approx 3.14 \):
\[ V_{\text{cylinder}} \approx 3.14 \times 11250 , \text{cm}^3 \approx 35325 , \text{cm}^3 \]
Step 2: Compare the Volumes
Now we’ll compare the two volumes obtained:
- Volume of the rectangular prism: \( 30000 , \text{cm}^3 \)
- Volume of the cylindrical tank: \( 35325 , \text{cm}^3 \)
Step 3: Conclusion
The volume of the cylindrical tank is \( 35325 , \text{cm}^3 \) which is greater than the volume of the rectangular prism tank, \( 30000 , \text{cm}^3 \).
Final Decision
Based on the calculated volumes, the cylindrical tank holds more water and should be the tank where Sophia should put her larger fish.