Subjects geometry

Cuboid Volume

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** We need to find the volume of a cuboid made up of small cubes, where the cuboid has dimensions 5 cm in height, 6 cm in width, and 7 cm in depth. 2. **Formula for volume of a cuboid:** The volume $V$ of a cuboid is given by the product of its length, width, and height: $$V = \text{length} \times \text{width} \times \text{height}$$ 3. **Apply the formula:** Here, length = 7 cm, width = 6 cm, and height = 5 cm. $$V = 7 \times 6 \times 5$$ 4. **Calculate the volume:** $$V = 42 \times 5 = 210$$ 5. **Interpretation:** The volume of the cuboid is 210 cubic centimetres, meaning it contains 210 small cubic units. **Final answer:** $$\boxed{210 \text{ cm}^3}$$