1. **State the problem:** Calculate the volume of a cuboid with given dimensions. 2. **Given dimensions:** - Length $l = 18$ cm - Height $h = 13$ cm - Diagonal of the front face $d = 23$ cm 3. **Find the width $w$:** The diagonal $d$ on the front face relates to height and width by the Pythagorean theorem: $$d^2 = h^2 + w^2$$ Substitute the known values: $$23^2 = 13^2 + w^2$$ $$529 = 169 + w^2$$ 4. **Solve for $w^2$:** $$w^2 = 529 - 169 = 360$$ 5. **Calculate $w$:** $$w = \sqrt{360} = \sqrt{36 \times 10} = 6\sqrt{10} \approx 18.97 \text{ cm}$$ 6. **Calculate the volume $V$ of the cuboid:** $$V = l \times w \times h$$ Substitute the values: $$V = 18 \times 6\sqrt{10} \times 13$$ 7. **Simplify the volume:** $$V = 18 \times 13 \times 6\sqrt{10} = 1404 \times \sqrt{10} \approx 1404 \times 3.162 = 4437.85 \text{ cm}^3$$ **Final answer:** The volume of the cuboid is approximately $4437.85$ cubic centimeters.