Answer:
The volume of Aquarium B.
Step-by-step explanation:
Let's denote the dimensions of the aquariums as follows:
- Aquarium A:
- Height: \( h_A \)
- Length: \( l_A \)
- Width: \( w \)
- Aquarium B:
- Height: \( h_B \)
- Length: \( l_B \)
- Width: \( w \)
According to the given information:
1. \( h_A = \frac{1}{2} h_B \)
2. \( l_B = 2 l_A \)
3. The widths of both aquariums are the same: \( w \)
Since both aquariums are rectangular, the volume of each aquarium is calculated by multiplying its height, length, and width.
For Aquarium A:
\[ V_A = h_A \times l_A \times w \]
For Aquarium B:
\[ V_B = h_B \times l_B \times w \]
Now, let's express \( h_A \) and \( l_B \) in terms of \( h_B \) and \( l_A \):
1. From \( h_A = \frac{1}{2} h_B \), we have \( h_B = 2h_A \).
2. From \( l_B = 2 l_A \), we have \( l_A = \frac{1}{2} l_B \).
Now we can calculate the volumes:
For Aquarium A:
\[ V_A = \left( \frac{1}{2} h_B \right) \times \left( \frac{1}{2} l_B \right) \times w = \frac{1}{4} h_B l_B w \]
For Aquarium B:
\[ V_B = h_B \times (2 l_A) \times w = 2 h_B l_A w = 2 h_B \left( \frac{1}{2} l_B \right) w = h_B l_B w \]
So, the volume of Aquarium A is \( \frac{1}{4} \) of the volume of Aquarium B.
