Let the breadth of the rectangular prism be \(x\) cm. \[ \therefore \text{Length} = 2x \text{ cm}, \quad \text{Height} = \frac{x}{2} \text{ cm} \] \[ \therefore 2(2x \times x + 2x \times \frac{x}{2} + \frac{x}{2} \times x) = 448 \Rightarrow 2(2x^2 + x^2 + \frac{x^2}{2}) = 448 \Rightarrow 2\left(\frac{4x^2 + 2x^2 + x^2}{2}\right) = 448 \Rightarrow 7x^2 = 448 \Rightarrow x^2 = 64 \Rightarrow x = 8 \] \[ \therefore \text{Volume of the prism} = x \times 2x \times \frac{x}{2} = x^3 \text{ cm}^3 = 8^3 \text{ cm}^3 = 512 \text{ cm}^3 \] \[ \therefore \text{The volume of the rectangular prism is } 512 \text{ cubic centimeters.} \]