1. **Stating the problem:** Find the volume of a cuboid given its total surface area is 300 cm², length $l=7$ cm, and breadth $b=16$ cm. 2. **Formula for surface area of a cuboid:** $$\text{Surface Area} = 2(lb + bh + hl)$$ where $h$ is the height. 3. **Substitute known values:** $$300 = 2(7 \times 16 + 16 \times h + h \times 7)$$ 4. **Simplify inside the parentheses:** $$300 = 2(112 + 16h + 7h)$$ $$300 = 2(112 + 23h)$$ 5. **Distribute 2:** $$300 = 224 + 46h$$ 6. **Isolate $h$ by subtracting 224 from both sides:** $$300 - 224 = 224 + 46h - 224$$ $$76 = 46h$$ 7. **Divide both sides by 46 to solve for $h$:** $$h = \frac{76}{46}$$ $$h = \frac{\cancel{76}^{38}}{\cancel{46}^{23}} = \frac{38}{23} \approx 1.652$$ 8. **Calculate the volume of the cuboid:** $$\text{Volume} = l \times b \times h = 7 \times 16 \times \frac{38}{23}$$ 9. **Multiply numerator:** $$7 \times 16 = 112$$ 10. **Volume:** $$\text{Volume} = \frac{112 \times 38}{23} = \frac{4256}{23} \approx 185.04 \text{ cm}^3$$ **Final answer:** The volume of the cuboid is approximately $185.04$ cubic centimeters.