1. **State the problem:** We need to find the volume of an L-shaped prism. It can be divided into two rectangular prisms: one big prism minus a smaller cutout prism. 2. **Identify dimensions:** - Big prism dimensions: height $10$ cm, width $6$ cm, length $16$ cm (total length) - Cutout prism dimensions: height $6$ cm, width $5$ cm, length $8$ cm 3. **Calculate volume of big prism:** $$V_{big} = \text{height} \times \text{width} \times \text{length} = 10 \times 6 \times 16 = 960 \text{ cm}^3$$ 4. **Calculate volume of cutout prism:** $$V_{cutout} = 6 \times 5 \times 8 = 240 \text{ cm}^3$$ 5. **Calculate volume of L-shaped prism:** Volume of L-shaped prism = volume of big prism minus volume of cutout prism $$V = V_{big} - V_{cutout} = 960 - 240 = 720 \text{ cm}^3$$ **Final answer:** The volume of the L-shaped prism is $720$ cubic centimeters.