To determine the volume of the space around the toy train in the box, let's break down the calculation step by step.
### Step 1: Calculate the Volume of the Box
The box is a right rectangular prism. The formula for the volume (V) of a rectangular prism is given by:
[tex]\[ V = \text{length} \times \text{width} \times \text{height} \][/tex]
Given:
- Length = 2 feet
- Width = [tex]\(1 \frac{1}{2}\)[/tex] feet = [tex]\(1 + \frac{1}{2}\)[/tex] feet = 1.5 feet
- Height = [tex]\(\frac{3}{4}\)[/tex] foot = 0.75 feet
So, the volume of the box is:
[tex]\[ V_{\text{box}} = 2 \times 1.5 \times 0.75 \][/tex]
[tex]\[ V_{\text{box}} = 2 \times 1.125 \][/tex]
[tex]\[ V_{\text{box}} = 2.25 \][/tex]
Thus, the volume of the box is 2.25 cubic feet.
### Step 2: Given Volume of the Toy Train
The volume of the toy train is given as 1 cubic foot.
### Step 3: Calculate the Volume of the Space Around the Toy Train
To find the volume of the space around the toy train, subtract the volume of the toy train from the volume of the box:
[tex]\[ V_{\text{space}} = V_{\text{box}} - V_{\text{train}} \][/tex]
Given:
- Volume of the box, [tex]\(V_{\text{box}}\)[/tex], is 2.25 cubic feet
- Volume of the toy train, [tex]\(V_{\text{train}}\)[/tex], is 1 cubic foot
Thus:
[tex]\[ V_{\text{space}} = 2.25 - 1 \][/tex]
[tex]\[ V_{\text{space}} = 1.25 \][/tex]
Therefore, the volume of the space around the toy train in the box is [tex]\(1 \frac{1}{4}\)[/tex] cubic feet.
The correct answer is:
[tex]\[ \boxed{1 \frac{1}{4}} \][/tex]
